-
-
Notifications
You must be signed in to change notification settings - Fork 2
/
Exercise_2_88.rkt
201 lines (170 loc) · 6.45 KB
/
Exercise_2_88.rkt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
#lang racket/base
(define table (make-hash))
(define (put op type item)
(hash-set! table (list op type) item))
(define (get op type)
(hash-ref! table (list op type) null))
(define (attach-tag type-tag contents)
(cond [(and (eq? type-tag 'scheme-number)
(number? contents))
contents]
[else (cons type-tag contents)]))
(define (type-tag datum)
(cond [(number? datum) 'scheme-number]
[(pair? datum) (car datum)]
[else null]))
(define (contents datum)
(cond [(number? datum) datum]
[(pair? datum) (cdr datum)]
[else (error "Bad tagged datum: CONTENTS" datum)]))
(define (apply-generic op . args)
(let ([type-tags (map type-tag args)])
(let ([proc (get op type-tags)])
(if (not (null? proc))
(apply proc (map contents args))
(error
"No method for these types: APPLY-GENERIC"
(list op type-tags))))))
(define (install-scheme-number-package)
(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))))
(put 'invert '(scheme-number)
(lambda (x) (tag (- x))))
(put 'make 'scheme-number (lambda (x) (tag x)))
'done)
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
(install-scheme-number-package)
(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))
(define (invert x) (apply-generic 'invert x))
(define (install-zero?-package)
(define (numer x) (car x))
(define (=zero?-ordinary x) (zero? x))
(define (=zero?-rational x) (zero? (numer x)))
(put '=zero? '(scheme-number) =zero?-ordinary)
(put '=zero? '(rational) =zero?-rational))
(install-zero?-package)
(define (=zero? x) (apply-generic '=zero? x))
(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)))
; representation of terms and term lists
(define (adjoin-term term term-list)
(if (=zero? (coeff term))
term-list
(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 (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 (sub-poly p1 p2)
(add-poly p1 (invert-poly p2)))
(define (invert-poly p)
(define (invert-terms terms)
(if (empty-termlist? terms)
terms
(let ([current-term (first-term terms)])
(adjoin-term (make-term (order current-term) (invert (coeff current-term)))
(invert-terms (rest-terms terms))))))
(make-poly (variable p) (invert-terms (term-list p))))
(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)
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 (+ (order t1) (order t2))
(mul (coeff t1) (coeff t2)))
(mul-term-by-all-terms t1 (rest-terms L))))))
(define (=zero?-poly x)
(define (check-terms terms)
(or (empty-termlist? terms) ; never happens, add-terms and mul-term-by-all-terms already checked
(and (=zero? (coeff (first-term terms)))
(check-terms (rest-terms terms)))))
(check-terms (term-list x)))
;; 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))))
(put '=zero? '(polynomial) =zero?-poly)
(put 'invert '(polynomial)
(lambda (p) (tag (invert-poly p))))
(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))
(define poly-a (make-polynomial 'x '((100 1) (2 2) (0 1))))
; '(polynomial x (100 1) (2 2) (0 1))
; x^100 + 2x^2 + 1
(sub poly-a poly-a)
; '(polynomial x)
(define poly-b (make-polynomial 'y '((1 1) (0 1))))
; '(polynomial y (1 1) (0 1))
; y + 1
(define poly-c (make-polynomial 'x (list (list 2 1) (list 1 poly-b) (list 0 5))))
; '(polynomial x (2 1) (1 (polynomial y (1 1) (0 1))) (0 5))
; x^2 + (y + 1)x + 5
(define poly-d (make-polynomial 'x '((2 1) (1 2) (0 1))))
; '(polynomial x (2 1) (1 2) (0 1))
; x^2 + 2x + 1
(sub poly-c poly-c)
; '(polynomial x)
(sub poly-a poly-d)
; '(polynomial x (100 1) (2 1) (1 -2))
; x^100 + x^2 - 2x