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#lang racket
(provide
make-interval
upper-bound
lower-bound
add-interval
mul-interval
div-interval
print-interval)
(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))))
(define (div-interval x 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 (lower-bound x) (car x))
(define (upper-bound x) (cdr x))
(define (print-interval x)
(newline)
(display "interval{")
(display (lower-bound x))
(display ",")
(display (upper-bound x))
(display "}")
(newline))
(define (print)
(define test-interval (make-interval 1 2))
(print-interval test-interval))
(print)
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