108 lines
2.5 KiB
Common Lisp
108 lines
2.5 KiB
Common Lisp
(defun add-rat (x y)
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(make-rat (+ (* (numer x) (denom y))
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(* (numer y) (denom x)))
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(* (denom x) (denom y))))
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(defun sub-rat (x y)
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(make-rat (- (* (numer x) (denom y))
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(* (numer y) (denom x)))
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(* (denom x) (denom y))))
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(defun mul-rat (x y)
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(make-rat (* (numer x) (numer y))
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(* (denom x) (denom y))))
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(defun div-rat (x y)
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(make-rat (* (numer x) (denom y))
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(* (numer y) (denom x))))
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(defun equal-ratp (x y)
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(= (* (numer x) (denom y))
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(* (numer y) (denom x))))
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(defun make-rat (n d)
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(let ((g (gcd n d)))
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(cons (/ n g) (/ d g))))
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(defun numer (x) (car x))
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(defun denom (x) (cdr x))
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(defun print-rat (x)
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(format t "~a/" (numer x))
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(format t "~a~%" (denom x)))
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;; Exercise 2.2
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(defun make-segment (start end)
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(cons
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(make-point (x-point start) (y-point start))
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(make-point (x-point end) (y-point end))))
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(defun start-segment (segment) (car segment))
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(defun end-segment (segment) (cdr segment))
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(defun average (x y)
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(/ (+ x y) 2))
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(defun midpoint-segment (segment)
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(make-point (average (x-point (start-segment segment))
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(x-point (end-segment segment)))
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(average (y-point (start-segment segment))
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(y-point (end-segment segment)))))
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(defun make-point (x y)
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(cons x y))
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(defun x-point (point) (car point))
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(defun y-point (point) (cdr point))
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(defun print-point (p)
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(format t "(~a,~a)~%" (x-point p) (y-point p)))
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;; Exercise 2.7
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(defun make-interval (a b)
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(cons a b))
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(defun lower-bound (x)
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(car x))
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(defun upper-bound (x)
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(cdr x))
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(defun add-interval (a b)
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(make-interval (+ (lower-bound a) (lower-bound b))
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(+ (upper-bound a) (upper-bound b))))
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(defun mul-interval (a b)
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(let ((p1 (* (lower-bound a) (lower-bound b)))
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(p2 (* (lower-bound a) (upper-bound b)))
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(p3 (* (upper-bound a) (lower-bound b)))
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(p4 (* (upper-bound a) (upper-bound b))))
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(make-interval (min p1 p2 p3 p4)
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(max p1 p2 p3 p4))))
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(defun div-interval (a b)
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(mul-interval
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a
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(make-interval (/ 1.0 (upper-bound b))
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(/ 1.0 (lower-bound b)))))
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;; Exercise 2.8
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(defun sub-interval (a b)
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(make-interval (- (lower-bound b) (lower-bound a))
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(- (upper-bound b) (upper-bound a))))
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;; Exercise 2.9
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(defun width-interval (x)
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"Calculate width of an interval as half of the distance between lower
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and upper bound."
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(/ (- (upper-bound x) (lower-bound x))
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2.0))
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;; Exercise 2.10
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(defun div-interval (a b)
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(if (zerop (width-interval b))
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(error "Cannot divide by 0 width interval")
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(mul-interval
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a
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(make-interval (/ 1.0 (upper-bound b))
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(/ 1.0 (lower-bound b))))))
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