(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 (mul-interval x y)
  ;;(cond ((and (> (lower-bound x) 0)
	      ;;(> (lower-bound y) 0))
	 ;;(make-interval 
	  ;;(* (lower-bound x))))))

(define (div-interval x y)
  (if (not (= (upper-bound y) (lower-bound y)))
    (mul-interval x 
		  (make-interval (/ 1.0 (upper-bound y))
				 (/ 1.0 (lower-bound y))))
    (begin
      (error "Error: second interval spans 0")
      (newline))))

(define (make-interval a b) (cons a b))

(define (lower-bound x) (car x))
(define (upper-bound x) (cdr x))

(define (sub-interval x y)
  (make-interval (- (lower-bound x) (upper-bound y))
		 (- (upper-bound x) (lower-bound y))))

;; 2.12
(define (make-centre-percent c p)
  (make-interval (- c (/ (* c p) 100))
		 (+ c (/ (* c p) 100))))

(define (center i)
  (/ (+ (lower-bound i) (upper-bound i)) 2))

(define (width i)
  (/ (- (upper-bound i) (lower-bound i)) 2))

(define (percent i)
  (* (/ (width i) (center i)) 100))


;; 2.14
;; parallel resistors

(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)))))