2.12
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (sub-interval x y)
(add-interval x (make-interval (- 0 (lower-bound y)) (- 0 (upper-bound y)))))
(define (mul-interval x y)
(let ((p1 (* (lower-bound x) (lower-bound y)))
(p2 (* (lower-bound x) (upper-bound y)))
(p3 (* (upper-bound x) (lower-bound y)))
(p4 (* (upper-bound x) (upper-bound y))))
(make-interval (min p1 p2 p3 p4)
(max p1 p2 p3 p4))))
(define (div-interval x y)
(let ((product-y (* (lower-bound y) (upper-bound y))))
(if (< product-y 0)
(display "illegal number")
(mul-interval x
(make-interval (/ 1.0 (upper-bound y)) (/ 1.0 (lower-bound y)))))))
(define (make-interval a b) (cons a b))
(define (lower-bound x) (car x))
(define (upper-bound x) (cdr x))
(define (interval-width interval)
(/ (- (upper-bound interval) (lower-bound interval)) 2))
(define (oper-interval-width v1 v2)
(let ((w1 (interval-width v1))
(w2 (interval-width v2)))
(lambda(x) (x w1 w2))))
(define (make-center-width c w)
(make-interval (- c w) (+ c w)))
(define (center i)
(/ (+ (lower-bound i) (upper-bound i)) 2))
(define (width i)
(/ (- (upper-bound i) (lower-bound i)) 2))
(define (make-center-percent c p)
(make-interval (- c (* c (/ p 100))) (+ c (* c (/ p 100)))))
(define (percent i)
(* 100 (/ (width i) (center i))))
(define interval-1 (make-center-percent 10 2))
(center interval-1)
(percent interval-1)
2.13
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (sub-interval x y)
(add-interval x (make-interval (- 0 (lower-bound y)) (- 0 (upper-bound y)))))
(define (mul-interval x y)
(let ((p1 (* (lower-bound x) (lower-bound y)))
(p2 (* (lower-bound x) (upper-bound y)))
(p3 (* (upper-bound x) (lower-bound y)))
(p4 (* (upper-bound x) (upper-bound y))))
(make-interval (min p1 p2 p3 p4)
(max p1 p2 p3 p4))))
(define (div-interval x y)
(let ((product-y (* (lower-bound y) (upper-bound y))))
(if (< product-y 0)
(display "illegal number")
(mul-interval x
(make-interval (/ 1.0 (upper-bound y)) (/ 1.0 (lower-bound y)))))))
(define (make-interval a b) (cons a b))
(define (lower-bound x) (car x))
(define (upper-bound x) (cdr x))
(define (interval-width interval)
(/ (- (upper-bound interval) (lower-bound interval)) 2))
(define (oper-interval-width v1 v2)
(let ((w1 (interval-width v1))
(w2 (interval-width v2)))
(lambda(x) (x w1 w2))))
(define (make-center-width c w)
(make-interval (- c w) (+ c w)))
(define (center i)
(/ (+ (lower-bound i) (upper-bound i)) 2))
(define (width i)
(/ (- (upper-bound i) (lower-bound i)) 2))
(define (make-center-percent c p)
(make-interval (- c (* c (/ p 100))) (+ c (* c (/ p 100)))))
(define (percent i)
(* 100 (/ (width i) (center i))))
(define interval-1 (make-center-percent 10 0.01))
(define interval-2 (make-center-percent 20 0.03))
(define interval-3 (mul-interval interval-1 interval-2))
(percent interval-3)
(define (par1 r1 r2)
(div-interval (mul-interval r1 r2)
(add-interval r1 r2)))
(define (par2 r1 r2)
(let ((one (make-interval 1 1)))
(div-interval one (add-interval (div-interval one r1)
(div-interval one r2)))))
(define r1 (make-center-percent 10 0.01))
(define r2 (make-center-percent 20 0.02))
(define r3 (par1 r1 r2))
(define r4 (par2 r1 r2))
(lower-bound r3)
(upper-bound r3)
(lower-bound r4)
(upper-bound r4)
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