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Implement 2.91 division

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Felix Martin 2020-11-29 22:30:30 -05:00
parent 262d0ed507
commit 164757c739
1 changed files with 43 additions and 43 deletions
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86
ex-2_77-97.scm
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@ -609,13 +609,17 @@
(error "Polys not in same var -- ADD-POLY"
(list p1 p2))))
(define (negate-term term)
(make-term (order term) (negate (coeff term))))
(define (negate-terms terms)
(map negate-term terms))
(define (sub-poly p1 p2)
(define (negate-term term)
(make-term (order term) (negate (coeff term))))
(if (same-variable? (variable p1) (variable p2))
(make-poly (variable p1)
(add-terms (term-list p1)
(map negate-term (term-list p2))))
(negate-terms (term-list p2))))
(error "Polys not in same var -- ADD-POLY"
(list p1 p2))))
@ -778,7 +782,8 @@
(attach-tag term-type (cdr terms))))
(define (empty-termlist? term-list) (null? (contents term-list)))
(define (make-term order coeff) (list order coeff))
(define (make-term order coeff)
(list order coeff))
(define (order term) (car term))
(define (coeff term) (cadr term))
@ -843,53 +848,48 @@
(define (div-poly p1 p2)
(if (same-variable? (variable p1) (variable p2))
(make-poly (variable p1)
(div-terms (term-list p1)
(term-list p2)))
(let ((result (div-terms (term-list p1) (term-list p2)))
(var (variable p1)))
(list
(tag (make-poly var (car result)))
(tag (make-poly var (cadr result)))))
(error "Polys not in same var -- MUL-POLY"
(list p1 p2))))
; Division can be performed via long division. That is, divide the highest-order
; term of the dividend by the highest-order term of the divisor. The result is
; the first term of the quotient. Next, multiply the result by the divisor,
; subtract that from the dividend, and produce the rest of the answer by
; recursively dividing the difference by the divisor. Stop when the order of the
; divisor exceeds the order of the dividend and declare the dividend to be the
; remainder. Also, if the dividend ever becomes zero, return zero as both
; quotient and remainder.
;
; We can design a div-poly procedure on the model of add-poly and mul-poly. The
; procedure checks to see if the two polys have the same variable. If so,
; div-poly strips off the variable and passes the problem to div-terms, which
; performs the division operation on term lists. Div-poly finally reattaches the
; variable to the result supplied by div-terms. It is convenient to design
; div-terms to compute both the quotient and the remainder of a division.
; Div-terms can take two term lists as arguments and return a list of the
; quotient term list and the remainder term list.
;
; dividend
; --------
; divisor
;
; Complete the following definition of div-terms by filling in the missing
; expressions. Use this to implement div-poly, which takes two polys as arguments
; and returns a list of the quotient and remainder polys.
; Division can be performed via long division. That is, divide the
; highest-order term of the dividend by the highest-order term of the
; divisor. The result is the first term of the quotient. Next, multiply the
; result by the divisor, subtract that from the dividend, and produce the
; rest of the answer by recursively dividing the difference by the divisor.
; Stop when the order of the divisor exceeds the order of the dividend and
; declare the dividend to be the remainder. Also, if the dividend ever
; becomes zero, return zero as both quotient and remainder.
(define (div-terms L1 L2)
(define (negate-term t)
(make-term (order t) (negate (coeff t))))
(define (negate-terms terms)
(let ((term-type (type-tag terms))
(term-list (contents terms)))
(cons term-type (map negate-term term-list))))
(if (empty-termlist? L1)
(list L1 L2)
(let ((t1 (first-term L1))
(t2 (first-term L2)))
(let ((t1 (first-term L1)) ; dividend
(t2 (first-term L2))) ; divisor
(if (> (order t2) (order t1))
(list (empty-termlist L2) L1)
(let ((new-c (div (coeff t1) (coeff t2)))
(new-o (- (order t1) (order t2)))
(new-term (make-term (- (order t1) (order t2))
(div (coeff t1) (coeff t2)))))
; XXX: continue here
(let ((rest-of-result (div-terms (empty-termlist L1) L2)))
(list (adjoin-term new-term (car rest-of-result))
(cadr rest-of-result))))))))
(let ((new-dividend (add-terms
L1
(negate-terms
(mul-terms
(adjoin-term new-term (empty-termlist L1))
L2)))))
(let ((rest-of-result (div-terms new-dividend L2)))
(list (adjoin-term new-term (car rest-of-result))
(cadr rest-of-result)))))))))
(define (=zero?-poly p)
(define (=zero?-terms terms)
@ -953,10 +953,10 @@
(define p2 (make-poly-dense 'x '((2 1) (0 -1))))
(assert (mul p1 p1) (make-poly-dense 'x '((10 1) (5 -2) (0 1))))
(assert (mul p1 p2) (make-poly-dense 'x '((7 1) (5 -1) (2 -1) (0 1))))
(display p1) (newline)
(display p2) (newline)
(display (div p1 p2)) (newline)
(let ((result (div p1 p2)))
(assert (car result) (make-poly-dense 'x '((3 1) (1 1))))
(assert (cadr result) (make-poly-dense 'x '((1 1) (0 -1)))))
(display "\nex-2.92\n")
;(display "\nex-2.93\n")