Solution to Exercise 1.30:

(define (sum term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (+ result (term a)))))
  (iter a 0))


Posted by Ken Dyck as Programming at 6:47 PM MST

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Solution to Exercise 1.29:

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))
 
(define (inc n) (+ n 1))
 
(define (simpsons-integral f a b n)
  (define (do-it h)
    (define (y k)
      (f (+ a (* k h))))
    (define (simpson-term k)
      (* (y k)
         (cond ((or (= k 0) (= k n)) 1)
               ((odd? k) 4)
               (else 2))))
    (* (/ h 3) (sum simpson-term 0 inc n)))
  (do-it (/ (- b a) n)))


Posted by Ken Dyck as Programming at 6:36 PM MST

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Posted by Ken Dyck as Books at 7:57 PM MST

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Solution to Exercise 1.28:

(define (square x)
  (* x x))
 
(define (expmod-with-trivial-sqrt-check base exp m)
  (cond ((= exp 0) 1)
        ((even? exp)
         (let* ((intermediate (expmod-with-trivial-sqrt-check base (/ exp 2) m))
                (squared-mod (remainder (square intermediate) m)))
           (if (and (not (or (= intermediate 1) (= intermediate (- m 1))))
                    (= squared-mod 1))
               0
               squared-mod)))
        (else
         (remainder (* base (expmod-with-trivial-sqrt-check base (- exp 1) m))
                    m))))
 
(define (miller-rabin-test n)
  (define (try-it a )
    (= (expmod-with-trivial-sqrt-check a (- n 1) n) 1))
  (try-it (+ 1 (random (- n 1)))))

Posted by Ken Dyck as Programming at 7:17 PM MST

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