带有通用型操作的系统
SICP 中文版P136：在设计大型系统时，
处理好一大批相互有关的类型而同时又能保持模块性，是一个非常困难的问题。
本文中的代码是完全体，可运行，书本上的操作全部验证通过；
包括 SICP 第二章第五节文本部分介绍的特性，及习题部分要求加入的新特性（除了
2.92）；
版本记录中包含此代码的文件是按照习题顺序逐次加入特性并提交的，需要按习题对照代
码及功能查看个人 github 页面的提交记录并检出：systems-with-generic-operations
运行程序的还需要 SICP 第三章 3.24 的习题代码，没有的请去上面的链接里往上翻。
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|
(load "../chapter3/3.24.scm")
;; make a type-operation table
(define tb (make-table equal?))
(define get (tb 'lookup-proc))
(define put (tb 'insert-proc!))
;; table done
;; overall general procedures
;; follow ex 2.78
(define (attach-tag type-tag contents)
(if (number? contents)
contents
(cons type-tag contents)))
(define (type-tag datum)
(cond ((number? datum) 'scheme-number)
((pair? datum) (car datum))
(else
(error "Bad tagged datum -- CONTENTS" datum))))
(define (contents datum)
(cond ((number? datum) datum)
((pair? datum) (cdr datum))
(else
(error "Bad tagged datum -- CONTENTS" datum))))
;; 2.78
;; follow 2.81
;; (define (apply-generic op . args)
;; (let ((type-tags (map type-tag args)))
;; (let ((proc (get op type-tags)))
;; (if proc
;; (apply proc (map contents args))
;; (if (= (length args) 2)
;; (let ((type1 (car type-tags))
;; (type2 (cadr type-tags))
;; (a1 (car args))
;; (a2 (cadr args)))
;; (if(equal? type1 type2)
;; (error "No method for these types"
;; (list op type-tags))
;; (let ((t1->t2 (get-coercion type1 type2))
;; (t2->t1 (get-coercion type2 type1)))
;; (cond (t1->t2
;; (apply-generic op (t1->t2 a1) a2))
;; (t2->t1
;; (apply-generic op a1 (t2->t1 a2)))
;; (else
;; (error "No method for these types"
;; (list op type-tags))))))
;; (error "No method for these types"
;; (list op type-tags))))))))
;; 2.81
;; follow ex 2.84
;; types-tower
(define (install-types-tower)
(put 'level 'scheme-number 1)
(put 'level 'rational 2)
;; real package is not implemented
(put 'level 'real 3)
(put 'level 'complex 4)
'done)
(define (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if proc
;; follow 2.85
;; (let ((res (apply proc (map contents args))))
;; (if (or (eq? op 'raise) (eq? op 'equ?) (eq? op '=zero?))
;; res
;; (drop res)))
;; 2.85
(apply proc (map contents args))
(if (= (length args) 2)
(let ((type1 (car type-tags))
(type2 (cadr type-tags))
(a1 (car args))
(a2 (cadr args)))
(cond ((equal? type1 type2)
(error "No method for these types"
(list op type-tags)))
((< (level a1) (level a2))
(apply-generic op (raise a1) a2))
(else (apply-generic op a1 (raise a2)))))
(error "No method for these types"
(list op type-tags)))))))
;; 2.84
(define (add x y) (apply-generic 'add x y))
(define (sub x y) (apply-generic 'sub x y))
(define (mul x y) (apply-generic 'mul x y))
(define (div x y) (apply-generic 'div x y))
;; follow ex 2.79
(define (equ? x y)(apply-generic 'equ? x y))
;; 2.79
;; follow ex 2.80
(define (=zero? x) (apply-generic '=zero? x))
;; 2.80
;; follow 2.83
(define (raise number) (apply-generic 'raise number))
;; 2.83
;; follow 2.84
(define (level x) (get 'level (type-tag x)))
;; 2.84
;; follow ex 2.85
(define (project x) (apply-generic 'project x))
(define (drop x)
(if (number? x)
x
(let ((a (project x)))
(if (equ? (raise a) x)
(drop a)
x))))
;; 2.85
;; follow ex 2.86
(define (sine x) (apply-generic 'sine x))
(define (cosine x) (apply-generic 'cosine x))
(define (arctan x) (apply-generic 'arctan x))
(define (exp x y) (apply-generic 'exp x y))
;; 2.86
;; follow ex 2.87
(define (negative n)
(apply-generic 'negative n))
;; 2.87
;; follow ex 2.93 & 2.94
(define (greatest-common-divisor a b)
(apply-generic 'gcd a b))
;; 2.93 & 2.94
;; follow ex 2.97
(define (reduce n d) (apply-generic 'reduce n d))
;; 2.97
;; helper functions
(define (square x) (mul x x))
(define (sqr x) (exp x 0.5))
;; built-in gcd
;; scheme-number package
(define (install-scheme-number-package)
(define (tag x)
(attach-tag 'scheme-number x))
;; follow ex 2.79
(define (equ-number? n1 n2)
(= n1 n2))
(put 'equ? '(scheme-number scheme-number) equ-number?)
;; 2,79
;; follow ex 2.80
(define (=zero-number? n) (= n 0))
(put '=zero? '(scheme-number) =zero-number?)
;; 2.80
;; follow 2.83
(define (scheme-number->rational number)
(make-rational number 1))
(put 'raise '(scheme-number) scheme-number->rational)
;; 2.83
;; follow 2.85
(define (drop-scheme-number x) x)
(put 'drop '(scheme-number) drop-scheme-number)
;; 2.85
;; follow ex 2.93 & 2.94
(define gcd-scheme-number gcd)
(put 'gcd '(scheme-number scheme-number)
(lambda (s1 s2) (tag (gcd-scheme-number s1 s2))))
;; 2.93 & 2.94
;; follow ex 2.97
(define (reduce-integers n d)
(let ((g (greatest-common-divisor n d)))
(list (div n g) (div d g))))
;; 2.97
(put 'reduce '(scheme-number scheme-number)
(lambda (n d) (map tag (reduce-integers n d))))
(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))))
(put 'make 'scheme-number
(lambda (x) (tag x)))
;; follow ex 2.86
(put 'sine '(scheme-number) (lambda (x) (tag (sin x))))
(put 'cosine '(scheme-number) (lambda (x) (tag (cos x))))
(put 'arctan '(scheme-number scheme-number) (lambda (y x) (tag (atan y x))))
(put 'exp '(scheme-number scheme-number) (lambda (x y) (tag (expt x y))))
;; 2.86
;; follow 2.88
(define (negative-scheme-number n)
(make-scheme-number (- n)))
(put 'negative '(scheme-number) negative-scheme-number)
;; 2.88
'done)
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
;; rational package
(define (install-rational-package)
;; internal procedures
(define (numer x) (car x))
(define (denom x) (cdr x))
;; (define (make-rat n d)
;; ;; follow ex 2.93 & 2.94
;; (let ((g (greatest-common-divisor n d)))
;; (cons (div n g) (div d g))))
;; follow ex 2.97
(define (make-rat n d)
(let ((simple (reduce n d)))
(cons (car simple) (cadr simple))))
;; 2.97
;; 2.93 & 2.94
(define (add-rat x y)
(make-rat (add (mul (numer x) (denom y))
(mul (numer y) (denom x)))
(mul (denom x) (denom y))))
(define (sub-rat x y)
(make-rat (sub (mul (numer x) (denom y))
(mul (numer y) (denom x)))
(mul (denom x) (denom y))))
(define (mul-rat x y)
(make-rat (mul (numer x) (numer y))
(mul (denom x) (denom y))))
(define (div-rat x y)
(make-rat (mul (numer x) (denom y))
(mul (denom x) (numer y))))
;; follow ex 2.79
(define (equ-rational? r1 r2)
(let ((product1 (* (numer r1) (denom r2)))
(product2 (* (denom r1) (numer r2))))
(= product1 product2)))
(put 'equ? '(rational rational) equ-rational?)
;; 2.79
;; follow ex 2.80
(define (=zero-rational? r)
(= (numer r) 0))
(put '=zero? '(rational) =zero-rational?)
;; 2.80
;; follow 2.83
;; note that we do not implement a real package
;; (define (rational->real number)
;; (make-real (/ (numer number) (denom number))))
;; (put 'raise '(rational) rational->real)
;; 2.83
;; follow 2.85
(define (project-rational x)
(make-scheme-number (round (/ (numer x) (denom x)))))
(put 'project '(rational) project-rational)
(define (drop-rational x)
(let ((a (project x)))
(if (equ? (raise a) x)
a
x)))
(put 'drop '(rational) drop-rational)
;; 2.85
;; follow 2.88
(define (negative-rational n)
(make-rational (negative (numer n)) (denom n)))
(put 'negative '(rational) negative-rational)
;; 2.88
;; interface to rest of the system
(define (tag x) (attach-tag 'rational x))
(put 'add '(rational rational)
(lambda (x y) (tag (add-rat x y))))
(put 'sub '(rational rational)
(lambda (x y) (tag (sub-rat x y))))
(put 'mul '(rational rational)
(lambda (x y) (tag (mul-rat x y))))
(put 'div '(rational rational)
(lambda (x y) (tag (div-rat x y))))
(put 'make 'rational
(lambda (n d) (tag (make-rat n d))))
;; follow ex 2.86
;; assume that there is a way of computing numer and denom from real number(*.*)
;; calls get_numer_denom, which returns a numer-denom pair
;; Alternative:
;; if not strictly stricted, sine/cosine/arctan/exp of rational could return scheme number;
;; just replace (tag (get_numer_denom)) with (make-scheme-number)
;; (put 'sine '(rational) (lambda (x) (tag (get_numer_denom (sine (/ (numer x) (denom x)))))))
;; (put 'cosine '(rational) (lambda (x) (tag (get_numer_denom (cosine (/ (numer x) (denom x)))))))
;; (put 'arctan '(rational rational)
;; (lambda (y x) (tag (get_numer_denom
;; (arctan (/ (numer y) (denom x)) (/ (numer x) (denom x)))))))
;; (put 'exp '(rational rational)
;; (lambda (x y) (tag (get_numer_denom
;; (exp (/ (numer x) (denom x)) (/ (numer y) (denom y)))))))
;; 2.86
'done)
(define (make-rational n d)
((get 'make 'rational) n d))
;; complex package
(define (install-complex-package)
;; imported procedures from rectangular and polar packages
(define (make-from-real-imag x y)
((get 'make-from-real-imag 'rectangular) x y))
(define (make-from-mag-ang r a)
((get 'make-from-mag-ang 'polar) r a))
;; internal procedures
(define (add-complex z1 z2)
(make-from-real-imag (add (real-part z1) (real-part z2))
(add (imag-part z1) (imag-part z2))))
(define (sub-complex z1 z2)
(make-from-real-imag (sub (real-part z1) (real-part z2))
(sub (imag-part z1) (imag-part z2))))
(define (mul-complex z1 z2)
(make-from-mag-ang (mul (magnitude z1) (magnitude z2))
(add (angle z1) (angle z2))))
(define (div-complex z1 z2)
(make-from-mag-ang (div (magnitude z1) (magnitude z2))
(sub (angle z1) (angle z2))))
;; follow ex 2.79
(define (equ-complex? c1 c2)
(let ((real1 (real-part c1))
(imag1 (imag-part c1))
(real2 (real-part c2))
(imag2 (imag-part c2)))
(and (= real1 real2) (= imag1 imag2))))
(put 'equ? '(complex complex) equ-complex?)
;; 2.79
;; follow ex 2.80
(define (=zero-complex? c)
(let ((real (real-part c))
(imag (imag-part c)))
(and (= real 0) (= imag 0))))
(put '=zero? '(complex) =zero-complex?)
;; 2.80
;; follow ex 2.85
;; need real package
;; (define (project-complex x) (make-real (real-part x)))
;; (put 'project '(complex) project-complex)
;; (define (drop-complex x)
;; (let ((a (project x)))
;; (if (equ? (raise a) x)
;; (drop a)
;; x)))
;; (put 'drop '(complex) drop-complex)
;; 2.85
;; follow ex 2.88
(define (negative-complex n)
(make-complex-from-real-imag (negative (real-part n)) (negative (imag-part n))))
(put 'negative '(complex) negative-complex)
;; 2.88
;; interface to rest of the system
(define (tag z) (attach-tag 'complex z))
(put 'add '(complex complex)
(lambda (z1 z2) (tag (add-complex z1 z2))))
(put 'sub '(complex complex)
(lambda (z1 z2) (tag (sub-complex z1 z2))))
(put 'mul '(complex complex)
(lambda (z1 z2) (tag (mul-complex z1 z2))))
(put 'div '(complex complex)
(lambda (z1 z2) (tag (div-complex z1 z2))))
(put 'make-from-real-imag 'complex
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'complex
(lambda (r a) (tag (make-from-mag-ang r a))))
'done)
;; rectangular-package for complex package
(define (install-rectangular-package)
;; internal procedures
(define (real-part z) (car z))
(define (imag-part z) (cdr z))
(define (make-from-real-imag x y) (cons x y))
(define (magnitude z)
(sqr (add (square (real-part z))
(square (imag-part z)))))
(define (angle z)
(atan (imag-part z) (real-part z)))
(define (make-from-mag-ang r a)
(cons (mul r (cosine a)) (mul r (sine a))))
;; interface to the rest of the system
(define (tag x) (attach-tag 'rectangular x))
(put 'real-part '(rectangular) real-part)
(put 'imag-part '(rectangular) imag-part)
(put 'magnitude '(rectangular) magnitude)
(put 'angle '(rectangular) angle)
(put 'make-from-real-imag 'rectangular
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'rectangular
(lambda (r a) (tag (make-from-mag-ang r a))))
'done)
;; polar-package for complex package
(define (install-polar-package)
;; internal procedures
(define (magnitude z) (car z))
(define (angle z) (cdr z))
(define (make-from-mag-ang r a) (cons r a))
(define (real-part z)
(mul (magnitude z) (cosine (angle z))))
(define (imag-part z)
(mul (magnitude z) (sine (angle z))))
(define (make-from-real-imag x y)
(cons (sqr (add (square x) (square y)))
(arctan y x)))
;; interface to the rest of the system
(define (tag x) (attach-tag 'polar x))
(put 'real-part '(polar) real-part)
(put 'imag-part '(polar) imag-part)
(put 'magnitude '(polar) magnitude)
(put 'angle '(polar) angle)
(put 'make-from-real-imag 'polar
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'polar
(lambda (r a) (tag (make-from-mag-ang r a))))
'done)
(define (real-part z) (apply-generic 'real-part z))
(define (imag-part z) (apply-generic 'imag-part z))
(define (magnitude z) (apply-generic 'magnitude z))
(define (angle z) (apply-generic 'angle z))
(define (make-complex-from-real-imag x y)
((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a)
((get 'make-from-mag-ang 'complex) r a))
;; follow ex 2.89 & 2.90
;; install common polynomial term package
(define (install-poly-term-package)
;; procedures kept same
(define (make-term order coeff) (list order coeff))
(define (order term) (car term))
(define (coeff term) (cadr term))
;; tag
(define (tag term)
(attach-tag 'polynomial-term term))
;; put
(put 'make 'polynomial-term
(lambda (x y) (tag (make-term x y))))
(put 'order '(polynomial-term) order)
(put 'coeff '(polynomial-term) coeff)
'done)
(define (make-term x y)
((get 'make 'polynomial-term) x y))
(define (order x)
(apply-generic 'order x))
(define (coeff x)
(apply-generic 'coeff x))
(define (install-dense-terms-package)
;; procedures about dense terms...
(define (tag terms)
(attach-tag 'polynomial-dense terms))
(define (first-term-d term-list)
(make-term (- (length term-list) 1) (car term-list)))
(define (rest-terms-d term-list) (cdr term-list))
(define (empty-termlist-d? term-list) (null? term-list))
(define (adjoin-term-d term term-list)
(cond ((=zero? (coeff term)) term-list)
((equ? (order term) (length term-list))
(cons (coeff term) term-list))
((> (order term) (length term-list))
(adjoin-term-d term (cons 0 term-list))))) ;
(define (negative-d terms)
(if (empty-termlist-d? terms)
terms
(let ((first (car terms)))
(cons (negative first)
(negative-d (rest-terms-d terms))))))
;; follow ex 2.96
(define (coeffs-d terms)
(cond ((empty-termlist-d? terms) '())
((equ? (car terms) 0) (coeffs-d (cdr terms)))
(else (cons (car terms) (coeffs-d (cdr terms))))))
(put 'coeffs '(polynomial-dense) coeffs-d)
;; 2.96
(put 'negative '(polynomial-dense)
(lambda (x) (tag (negative-d x))))
(put 'first-term '(polynomial-dense)
(lambda (x) (first-term-d x)))
(put 'empty-termlist? '(polynomial-dense) empty-termlist-d?)
(put 'rest-terms '(polynomial-dense)
(lambda (x) (tag (rest-terms-d x))))
(put 'adjoin-term 'polynomial-dense
(lambda (x y) (tag (adjoin-term-d x y))))
(put 'make 'polynomial-dense (lambda (t) (tag t)))
'done)
(define (make-dense-terms terms)
((get 'make 'polynomial-dense) terms))
(define (install-sparse-terms-package)
;; procedures about sparse terms...
(define (tag terms)
(attach-tag 'polynomial-sparse terms))
(define (first-term-s term-list) (car term-list))
(define (adjoin-term-s term term-list)
(if (=zero? (coeff term))
term-list
(cons term term-list)))
(define (rest-terms-s term-list) (cdr term-list))
(define (empty-termlist-s? term-list) (null? term-list))
(define (negative-s terms)
(if (empty-termlist-s? terms)
terms
(let ((first (first-term-s terms)))
(adjoin-term-s (make-term
(order first)
(negative (coeff first)))
(negative-s (rest-terms-s terms))))))
;; follow ex 2.96
(define (coeffs-s terms)
(map (lambda (t) (coeff t)) terms))
(put 'coeffs '(polynomial-sparse) coeffs-s)
;; 2.96
(put 'negative '(polynomial-sparse)
(lambda (x) (tag (negative-s x))))
(put 'first-term '(polynomial-sparse)
(lambda (x) (first-term-s x)))
(put 'empty-termlist? '(polynomial-sparse) empty-termlist-s?)
(put 'rest-terms '(polynomial-sparse)
(lambda (x) (tag (rest-terms-s x))))
(put 'adjoin-term 'polynomial-sparse
(lambda (x y) (tag (adjoin-term-s x y))))
(put 'make 'polynomial-sparse (lambda (t) (tag t)))
'done)
(define (make-sparse-terms terms)
((get 'make 'polynomial-sparse) terms))
(define (first-term x)
(apply-generic 'first-term x))
(define (adjoin-term x y)
((get 'adjoin-term (type-tag y)) x (contents y)))
(define (negative x)
(apply-generic 'negative x))
(define (empty-termlist? x)
(apply-generic 'empty-termlist? x))
(define (rest-terms x)
(apply-generic 'rest-terms x))
(define (make-terms t terms)
((get 'make t)
(if (equal? t 'polynomial-sparse)
terms
(map coeff terms))))
;; 2.89 & 2.90
;; follow 2.96
(define (coeffs t)
(apply-generic 'coeffs t))
;; 2.96
;; polynomial-package
(define (install-polynomial-package)
;; internal procedures
;; representation of poly
(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)))
;; terms
(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)
L1
(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)
L
(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))))))
;; follow ex 2.91
(define (div-terms L1 L2)
(if (empty-termlist? L1)
(list L1 L1)
(let ((t1 (first-term L1))
(t2 (first-term L2)))
(if (> (order t2) (order t1))
(list (make-terms (type-tag L1) '()) L1)
(let ((new-c (div (coeff t1) (coeff t2)))
(new-o (sub (order t1) (order t2))))
(let ((rest-of-result
(div-terms
(add-terms L1
(negative (mul-term-by-all-terms
(make-term new-o new-c)
L2)))
L2)))
(list (adjoin-term (make-term new-o new-c)
(car rest-of-result))
(cadr rest-of-result))))))))
;; follow ex 2.96
(define (pseudoremainder-terms a b)
(let ((f1 (first-term a))
(f2 (first-term b)))
(let ((o1 (order f1))
(o2 (order f2))
(c (coeff f2)))
(let ((constant (exp c (+ 1 o1 (- o2)))))
(let ((term (make-term 0
constant)))
(cadr (div-terms
(mul-term-by-all-terms term a)
b)))))))
(define (gcd-terms-coeff l)
(define (recursive l)
(cond ((= 2 (length l))
(greatest-common-divisor (car l) (cadr l)))
((= 1 (length l)) (car l))
((null? l) 0)
(else (greatest-common-divisor
(car l)
(recursive (cdr l))))))
(recursive l))
(define (gcd-terms a b)
(if (empty-termlist? b)
(let ((coeffs-gcd (gcd-terms-coeff (coeffs a))))
(car (div-terms
a
(make-terms (type-tag a)
(list (make-term 0 coeffs-gcd))))))
(gcd-terms b (pseudoremainder-terms a b))))
;; 2.96
;; follow 2.97
(define (reduce-terms n d)
(define (compute-constant a b c)
(let ((af (first-term a))
(bf (first-term b))
(cf (first-term c)))
(let ((c (coeff af))
(o1 (max (order bf) (order cf)))
(o2 (order af)))
(exp c (+ 1 o1 (- o2))))))
(define (simplify a b)
(let ((g (gcd-terms-coeff (append (coeffs a) (coeffs b)))))
(let ((divider (make-terms (type-tag a) (list (make-term 0 g)))))
(list (car (div-terms a divider)) (car (div-terms b divider))))))
(let ((g (gcd-terms n d)))
(let ((constant (compute-constant g n d)))
(let ((mn (mul-term-by-all-terms (make-term 0 constant) n))
(md (mul-term-by-all-terms (make-term 0 constant) d)))
(let ((gn (car (div-terms mn g)))
(gd (car (div-terms md g))))
(simplify gn gd))))))
(define (reduce-poly p1 p2)
(if (same-variable? (variable p1) (variable p2))
(let ((t1 (term-list p1))
(t2 (term-list p2)))
(let ((result (reduce-terms t1 t2)))
(list (make-poly (variable p1) (car result))
(make-poly (variable p1) (cadr result)))))
(error "Polys not in same variable -- REDUCE-POLY"
(list p1 p2))))
(put 'reduce '(polynomial polynomial)
(lambda (n d) (map tag (reduce-poly n d))))
;; 2.97
;; 2.91
;; follow ex 2.87
(define (=zero?-p p)
(define (recursive terms)
(if (empty-termlist? terms)
#t
(let ((first (first-term terms))
(rest (rest-terms terms)))
(if (=zero? (coeff first))
(recursive rest)
#f))))
(recursive (term-list p)))
(put '=zero? '(polynomial) =zero?-p)
;; 2.87
;; poly
;; follow 2.88
(define (negative-poly n)
(make-poly (variable n) (negative (term-list n))))
(put 'negative '(polynomial)
(lambda (x) (tag (negative-poly x))))
(define (sub-poly p1 p2)
(add-poly p1 (negative-poly p2)))
(put 'sub '(polynomial polynomial)
(lambda (x y) (tag (sub-poly x y))))
;; 2.88
(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))))
;; follow 2.91
(define (div-poly p1 p2)
(if (same-variable? (variable p1) (variable p2))
(let ((t1 (term-list p1))
(t2 (term-list p2)))
(let ((result (div-terms t1 t2)))
(make-poly (variable p1)
(car result))))
(error "Polys not in same var -- DIV-POLY"
(list p1 p2))))
(put 'div '(polynomial polynomial)
(lambda (p1 p2) (tag (div-poly p1 p2))))
;; 2.91
;; follow 2.93 & 2.94
(define (gcd-poly a b)
;; (define (remainder-terms t1 t2)
;; (cadr (div-terms t1 t2)))
;; (define (gcd-terms t1 t2)
;; (if (empty-termlist? t2)
;; t1
;; (gcd-terms t2 (remainder-terms t1 t2))))
(if (same-variable? (variable a) (variable b))
(let ((t1 (term-list a))
(t2 (term-list b)))
(make-poly (variable a) (gcd-terms t1 t2)))
(error "Polys not in same var -- GCD-POLY"
(list a b))))
(put 'gcd '(polynomial polynomial)
(lambda (p1 p2) (tag (gcd-poly p1 p2))))
;; 2.93 & 2.94
;; interface to rest of the system
(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))))
'done)
(define (make-polynomial var terms)
((get 'make 'polynomial) var terms))
;; install
(install-types-tower)
(install-scheme-number-package)
(install-rational-package)
(install-rectangular-package)
(install-polar-package)
(install-complex-package)
(install-poly-term-package)
(install-dense-terms-package)
(install-sparse-terms-package)
(install-polynomial-package)
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