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;; 2.1.4 Extended Exercise:Interval Arithmetic
(define (add-interval x y)
(make-interval (+ (lower-bound x)
(lower-bound y))
(+ (upper-bound x)
(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))))
;; Todo:ensure this is right
(define (div-interval x y)
(if (>= 0 (* (lower-bound y) (upper-bound y)))
(error "error!" y)
(mul-interval x
(make-interval
(/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))
(define (make-interval a b) (cons a b))
;; Exercise:2.7
;; My version
;; (define (lower-bound interval) (car interval))
;; (define (upper-bound interval) (cdr interval))
(define (lower-bound interval) (min (car interval)
(cdr interval)))
(define (upper-bound interval) (max (car interval)
(cdr interval)))
;; ???
;; Exercise:2.8
(define (sub-interval x y)
(make-interval (- (lower-bound x) (upper-bound y))
(- (upper-bound x) (lower-bound y))))
(define (display-interval i)
(newline)
(display "[")
(display (lower-bound i))
(display ",")
(display (upper-bound i))
(display "]"))
(define i (make-interval 1 5))
(define j (make-interval 1 4))
(display-interval i)
(display-interval (sub-interval i j))
(display-interval (sub-interval j i))
;; Exercise:2.9
(define (interval-width i)
(/ (- (upper-bound i) (lower-bound i))
2))
(interval-width (make-interval 2 8))
;; Exercise:2.10
(define (div-interval x y)
(if (>= 0 (* (lower-bound y) (upper-bound y)))
(error "error!" y)
(mul-interval x
(make-interval
(/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))
(define (make-interval a b) (cons a b))
(define span-0 (make-interval -1 2))
(display-interval (div-interval i j))
(display-interval (div-interval i span-0))
;; Exercise:2.11
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