Month: May 2007

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))


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)))


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)))))