# 2.14

## 练习 2.14 请确认 Len 是对的。请你用各种不同的算术表达式来检查这一系统的行为。请做出两个区间 A 和 B，并用它们计算表达式 A/A 和 A/B。如果所用区间的宽度相对于中心值取很小百分数，你将会得到更多的认识。请检查对于中心-百分比形式（见练习2.12）进行计算的结果。

(define (make-interval a b) (cons a b))
(define upper-bound cdr)
(define lower-bound car)
(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 (upper-bound y)) (- 0 (lower-bound y)))))
(define (subtract-interval x y)
(define p1 (- (lower-bound x) (lower-bound y)))
(define p2 (- (lower-bound x) (upper-bound y)))
(define p3 (- (upper-bound x) (lower-bound y)))
(define p4 (- (upper-bound x) (upper-bound y)))

(make-interval (min p1 p2 p3 p4) (max p1 p2 p3 p4)))

(define (mul-interval x y)
(define p1 (* (lower-bound x) (lower-bound y)))
(define p2 (* (lower-bound x) (upper-bound y)))
(define p3 (* (upper-bound x) (lower-bound y)))
(define p4 (* (upper-bound x) (upper-bound y)))

(make-interval (min p1 p2 p3 p4) (max p1 p2 p3 p4))
)

(define (div-interval x y)
(if (<= (* (lower-bound y) (upper-bound y)) 0) "Not allowed!"
(mul-interval x
(make-interval (/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))

(define int1 (make-interval 2 4))
(define int2 (make-interval 3 6))
int1

int2

(define (par1 r1 r2)
(div-interval (mul-interval r1 r2) (add-interval r1 r2)))
(define (par2 r1 r2)
(define one (make-interval 1 1))
(div-interval one (add-interval (div-interval one r1) (div-interval one r2))))
(par1 int1 int2)

(par2 int1 int2)


(define A int1)
(define B int2)

(div-interval A A)

(div-interval A B)


(define AA (make-interval 99 100))
(define BB (make-interval 999 1000))
(div-interval AA AA)

(div-interval AA BB)


(define (make-center-percent center percent)
(make-interval (- center (* center percent))
(+ center (* center percent))))

(define (center x) (/ (+ (lower-bound x) (upper-bound x)) 2))
(define (width x) (/ (- (upper-bound x) (lower-bound x)) 2))

(define (percent x)
(/ (width x) (center x)))

(define AAAA (make-center-percent (center A) (percent A)))
(define BBBB (make-center-percent (center B) (percent B)))

(div-interval AAAA AAAA)

(div-interval AAAA BBBB)


(define make-c-p cons)
(define c car)
(define p cdr)
(define (w x) (* (c x) (p x)))

(define (center x) (/ (+ (lower-bound x) (upper-bound x)) 2))
(define (width x) (/ (- (upper-bound x) (lower-bound x)) 2))
(define (percent x) (/ (width x) (center x)))

(define AAA (make-c-p (center A) (percent A)))
AAA

(define BBB (make-c-p (center B) (percent B)))
BBB

(div-interval AAA AAA)

(div-interval AAA BBB)