scheme - SICP exercise 3.62 -

i've been finished exercise 3.59, 3.60, 3.61 , stuck @ 3.62, turn sicp-solutions@scheme wiki community help.

exercise 3.59 , 3.60 tested sine , cosine case, not 3.61 or 3.62.

the 3.62 code provided on community produces all-zero tangent series on condition of correct sine , cosine series:

> (display-stream-until sine-series 7) 0 1 0 -1/6 0 1/120 0  > (display-stream-until cosine-series 7) 1 0 -1/2 0 1/24 0 -1/720  > (display-stream-until tangent-series 7) 0 0 0 0 0 0 0 

at first think code wrote in previous exercises might wrong, check solutions of 3.59/3.60/3.61 on community , turn out produce same result.

i try copying code of 3.59/3.60/3.61 ide(drracket) , still tangent series printed zero.

here code:

(define (mul-series s1 s2)   (cons-stream (* (stream-car s1)                   (stream-car s2))                (add-streams (mul-streams (stream-cdr s1)                                          (stream-cdr s2))                             (mul-series s1 s2))))  (define (reciprocal-series s)   (cons-stream 1                (scale-stream (mul-series (stream-cdr s)                                          (reciprocal-series s))                              -1)))  (define (div-series s1 s2)   (let ((c (stream-car s2)))     (if (= c 0)         (error "constant term of s2 can't 0!")         (scale-stream          (mul-series s1                      (reciprocal-series (scale-stream s2                      (/ 1 c))))      (/ 1 c)))))  (define tangent-series   (div-series sine-series               cosine-series)) 

and requiring part: (too long highlight body)

(require (only-in "mylib.rkt"                   cons-stream                   stream-car                   stream-cdr                   add-streams                   mul-streams                   scale-stream                   stream-map                   ones                   integers                   sine-series                   cosine-series                   stream-ref                   display-stream-until)) 

could tell me what's wrong code or might possible bugs hide?

by way, how guys verify code on sicp?

i've found several blog/github repository provide code without (enough) testing case(s).

i have hard time dealing such mathematics questions bare code.

the problem mul-series.
product of series [a₀ + a₁x + ...] , series [b₀ + b₁x + ...] is
    [a₀b₀ + (a₀b₁ + a₁b₀)x + ...]
mul-series produces
    (cons-stream a₀b₀ (add-streams (mul-streams (cdr s1) (cdr s2)) (mul-series s1 s2)))
     = (cons-stream a₀b₀ (add-streams [a₁b₁, ...] [a₀b₀, ...]))
     = [a₀b₀, a₁b₁ + a₀b₀, ...]

you can check mul-series using identity sin(x)² + cos(x)² = 1 (as suggested in exercise 3.60).
other simple test cases try are
    [2] * [0 + x] = [0 + 2x]
    [1 + x] * [1 + x] = [ 1 + 2x + 1x²]

with appropriate helper functions, tests this:

> (show-series (add-streams (mul-series sine-series sine-series) (mul-series cosine-series cosine-series))) 1 + 0*x + 0*x^2 + ... > (show-series (mul-series (make-series '(2)) (make-series '(0 1)))) 0 + 2*x + ... > (show-series (mul-series (make-series '(1 1)) (make-series '(1 1)))) 1 + 2*x + 1*x^2 + ... 

here helper functions i've defined:

(define zeroes (cons-stream 0 zeroes))  ;; make-series takes list of numbers , returns infinite stream ;; numbers followed 0's (define (make-series coeffs)   (if (null? coeffs)       zeroes       (cons-stream (car coeffs) (make-series (cdr coeffs)))))  ;; show-stream prints first 10 items in stream (define (show-stream stream)   (begin (show-stream-helper stream 10)))  (define (show-stream-helper stream n)   (if (= 0 n)       (begin (display "...")              (newline))       (begin (display (stream-car stream))              (display ", ")              (show-stream-helper (stream-cdr stream) (- n 1)))))  ;; show-series show-stream, uses format a0 + a1*x + ... (define (show-series stream)   (show-series-helper stream 0 10))  (define (show-series-helper stream n m)   (if (> n m)       (begin (display "...")              (newline))       (begin (show-monomial (stream-car stream) n)              (display " + ")              (show-series-helper (stream-cdr stream) (+ 1 n) m))))  ;; show-monomial displays a*x^n (define (show-monomial coeff pow)   (cond    ((= 0 pow)     (display coeff))    ((= 1 pow)     (display coeff)     (display "*x"))    (else     (display coeff)     (display "*x^")     (display pow))))