►zthomae’s SICP solutions
▼3 Chapter 3
3.1 Exercise 3.1
3.2 Exercise 3.2
3.3 Exercise 3.3
3.4 Exercise 3.4
3.5 Exercise 3.5
3.6 Exercise 3.6
3.7 Exercise 3.7
3.8 Exercise 3.8
3.9 Exercise 3.9
3.10 Exercise 3.10
3.11 Exercise 3.11
3.12 Exercise 3.12
3.13 Exercise 3.13
3.14 Exercise 3.14
3.15 Exercise 3.15
3.16 Exercise 3.16
3.17 Exercise 3.17
3.18 Exercise 3.18
3.19 Exercise 3.19
3.20 Exercise 3.20
3.21 Exercise 3.21
3.22 Exercise 3.22
3.23 Exercise 3.23
3.24 Exercise 3.24
3.25 Exercise 3.25
3.26 Exercise 3.26
3.27 Exercise 3.27
3.28 Exercise 3.28
3.29 Exercise 3.29
3.30 Exercise 3.30
3.31 Exercise 3.31
3.32 Exercise 3.32
3.33 Exercise 3.33
3.34 Exercise 3.34
3.35 Exercise 3.35
3.36 Exercise 3.36
3.37 Exercise 3.37
3.38 Exercise 3.38
3.39 Exercise 3.39
3.40 Exercise 3.40
3.41 Exercise 3.41
3.42 Exercise 3.42
3.43 Exercise 3.43
3.44 Exercise 3.44
3.45 Exercise 3.45
3.46 Exercise 3.46
3.47 Exercise 3.47
3.48 Exercise 3.48
3.49 Exercise 3.49
3.50 Exercise 3.50
3.51 Exercise 3.51
3.52 Exercise 3.52
3.53 Exercise 3.53
3.54 Exercise 3.54
3.55 Exercise 3.55
3.56 Exercise 3.56
3.57 Exercise 3.57
3.58 Exercise 3.58
3.59 Exercise 3.59
3.60 Exercise 3.60
3.61 Exercise 3.61
3.62 Exercise 3.62
3.63 Exercise 3.63
3.64 Exercise 3.64
3.65 Exercise 3.65
3.66 Exercise 3.66
3.67 Exercise 3.67
3.68 Exercise 3.68
3.69 Exercise 3.69
3.70 Exercise 3.70
3.71 Exercise 3.71
3.72 Exercise 3.72
3.73 Exercise 3.73
3.74 Exercise 3.74
3.75 Exercise 3.75
3.76 Exercise 3.76
3.77 Exercise 3.77
3.78 Exercise 3.78
3.79 Exercise 3.79
3.80 Exercise 3.80
3.81 Exercise 3.81
3.82 Exercise 3.82
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3.69 Exercise 3.69

We can define triples similarly to how we defined pairs, constructing a new triplet by consing an element i onto a pair (j, k) as long as i <= j.

(define (triples s t u)
  (if (or (stream-null? s) (stream-null? t) (stream-null? u))
      the-empty-stream
      (cons-stream
       (list (stream-car s) (stream-car t) (stream-car u))
       (interleave
        (stream-map (lambda (p) (cons (stream-car s) p))
                    (pairs (stream-cdr t) (stream-cdr u)))
        (triples (stream-cdr s) (stream-cdr t) (stream-cdr u))))))

We can then find all Pythagorean triples as follows:

(define pythagorean-triples
  (stream-filter
   (lambda (triple)
     (let ((i (car triple))
           (j (cadr triple))
           (k (caddr triple)))
       (= (+ (square i) (square j)) (square k))))
   (triples integers integers integers)))
> (display-stream (take-stream pythagorean-triples 5))

(3 4 5)

(6 8 10)

(5 12 13)

(9 12 15)

(8 15 17)

'done

However, this might not be exactly what we want, as allows non-primitive triples as well (for examples, (6, 8, 10} as well as (3, 4, 5). We can use another stream filter to account for this as well.

(define primitive-pythagorean-triples
  (stream-filter
   (lambda (triple)
     (let ((i (car triple))
           (j (cadr triple))
           (k (caddr triple)))
       (= 1 (gcd i (gcd j k)))))
   pythagorean-triples))
> (display-stream (take-stream primitive-pythagorean-triples 2))

(3 4 5)

(5 12 13)

'done

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