set-3

Exercise 2.93

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Modify the rational-arithmetic package to use generic operations, but change make-rat so that it does not attempt to reduce fractions to lowest terms. Test your system by calling make-rational on two polynomials to produce a rational function

(define p1 (make-polynomial 'x '((2 1)(0 1))))
(define p2 (make-polynomial 'x '((3 1)(0 1))))
(define rf (make-rational p2 p1))

Now add rf to itself, using add. You will observe that this addition procedure does not reduce fractions to lowest terms.

Exercise 2.66

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Implement the lookup procedure for the case where the set of records is structured as a binary tree, ordered by the numerical values of the keys.

Exercise 2.46

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A two-dimensional vector v running from the origin to a point can be represented as a pair consisting of an x-coordinate and a y-coordinate. Implement a data abstraction for vectors by giving a constructor make-vect and corresponding selectors xcor-vect and ycor-vect. In terms of your selectors and constructor, implement procedures add-vect, sub-vect, and scale-vect that perform the operations vector addition, vector subtraction, and multiplying a vector by a scalar:

Exercise 2.47

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Here are two possible constructors for frames:

(define (make-frame origin edge1 edge2)
  (list origin edge1 edge2))

(define (make-frame origin edge1 edge2)
  (cons origin (cons edge1 edge2)))

For each constructor supply the appropriate selectors to produce an implementation for frames.

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