Implement till 2.87
parent
d9676999ef
commit
bc6bd8b007
126
ex-2_77-97.scm
126
ex-2_77-97.scm
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@ -543,8 +543,130 @@
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(display (add cr cr)) (newline)
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(display (mul cr cr)) (newline)
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(display "\n\nexample - symbolic algebra\n")
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(display "\nexample - symbolic algebra\n")
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(display "\nex-2.87\n")
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(define (install-polynomial-package)
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;; internal procedures
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;; representation of poly
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(define (make-poly variable term-list)
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(cons variable term-list))
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(define (variable p) (car p))
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(define (term-list p) (cdr p))
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;; procedures same-variable? and variable? from section 2.3.2
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(define (variable? x) (symbol? x))
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(define (=number? exp num)
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(and (number? exp) (= exp num)))
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(define (same-variable? v1 v2)
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(and (variable? v1) (variable? v2) (eq? v1 v2)))
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;; representation of terms and term lists
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(define (adjoin-term term term-list)
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(if (=zero? (coeff term))
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term-list
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(cons term term-list)))
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(define (the-empty-termlist) '())
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(define (first-term term-list) (car term-list))
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(define (rest-terms term-list) (cdr term-list))
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(define (empty-termlist? term-list) (null? term-list))
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(define (make-term order coeff) (list order coeff))
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(define (order term) (car term))
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(define (coeff term) (cadr term))
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(define (add-terms L1 L2)
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(cond ((empty-termlist? L1) L2)
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((empty-termlist? L2) L1)
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(else
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(let ((t1 (first-term L1)) (t2 (first-term L2)))
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(cond ((> (order t1) (order t2))
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(adjoin-term
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t1 (add-terms (rest-terms L1) L2)))
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((< (order t1) (order t2))
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(adjoin-term
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t2 (add-terms L1 (rest-terms L2))))
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(else
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(adjoin-term
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(make-term (order t1)
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(add (coeff t1) (coeff t2)))
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(add-terms (rest-terms L1)
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(rest-terms L2)))))))))
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(define (add-poly p1 p2)
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(if (same-variable? (variable p1) (variable p2))
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(make-poly (variable p1)
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(add-terms (term-list p1)
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(term-list p2)))
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(error "Polys not in same var -- ADD-POLY"
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(list p1 p2))))
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(define (mul-terms L1 L2)
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(if (empty-termlist? L1)
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(the-empty-termlist)
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(add-terms (mul-term-by-all-terms (first-term L1) L2)
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(mul-terms (rest-terms L1) L2))))
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(define (mul-term-by-all-terms t1 L)
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(if (empty-termlist? L)
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(the-empty-termlist)
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(let ((t2 (first-term L)))
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(adjoin-term
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(make-term (+ (order t1) (order t2))
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(mul (coeff t1) (coeff t2)))
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(mul-term-by-all-terms t1 (rest-terms L))))))
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(define (mul-poly p1 p2)
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(if (same-variable? (variable p1) (variable p2))
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(make-poly (variable p1)
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(mul-terms (term-list p1)
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(term-list p2)))
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(error "Polys not in same var -- MUL-POLY"
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(list p1 p2))))
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(define (=zero?-poly p)
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(define (=zero?-terms terms)
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(cond
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((empty-termlist? terms) #t)
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((not (=zero? (coeff (first-term terms)))) #f)
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(else (=zero?-terms (rest-terms terms)))))
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(=zero?-terms (term-list p)))
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;; interface to rest of the system
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(define (tag p) (attach-tag 'polynomial p))
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(put 'add '(polynomial polynomial)
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(lambda (p1 p2) (tag (add-poly p1 p2))))
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(put 'mul '(polynomial polynomial)
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(lambda (p1 p2) (tag (mul-poly p1 p2))))
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(put '=zero? '(polynomial) =zero?-poly)
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(put 'make 'polynomial
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(lambda (var terms) (tag (make-poly var terms))))
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(display "[install-polynomial-package]\n")
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'done)
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(install-polynomial-package)
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(define (make-poly var terms)
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((get 'make 'polynomial) var terms))
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(define p (make-poly 'x '((100 2) (1 2))))
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;(display p)
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(assert (mul p p)
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(make-poly 'x '((200 4) (101 8) (2 4))))
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(display "\nex-2.87 - =zero?\n")
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(assert (=zero? p) #f)
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(assert #t
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(=zero? (make-poly 'x (list
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(list 10 (make-rational 0 10))
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(list 5 (make-complex-from-real-imag 0 0))
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(list 1 0)))))
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(define px p)
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(define py (make-poly 'y (list (list 3 px))))
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(display (add py py))
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(newline)
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(display "\nex-2.88 - sub\n")
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