sicp-ex-3.62

A simple solution, that produces the right tangent power series coefficients when displayed

  
  
 ;nums is numerator, dems is denominator 
  
 (define (div-series nums dems) 
   (mul-series nums 
               (invert-series dems))) 
  
 (define tangent-series (div-series sine-series cosine-series)) 

Source for the correct tangent power series: https://socratic.org/questions/what-is-the-taylor-series-expansion-for-the-tangent-function-tanx

(define (div-series s1 s2)
  (let ((c (stream-car s2)))
    (if (= c 0)
        (error "constant term of s2 can't be 0!")
        (scale-stream (mul-series s1
                                  (reciprocal-series (scale-stream s2 (/ 1 c))))
                      (/ 1 c)))))

(define tane-series (div-series sine-series cosine-series))

; according 3-61
; S·X = 1
; X = 1 / S
; another S1
; S1 / S  =  S1 · X

;use code in 3-61
(load "3-61.scm")
;"daoshu" mean reciprocal

(define (div-series s1 s2)
    (cond ((eq? 0 (stream-car s2)) (error "constant term of s2 can't be 0!"))
          (else (mul-series s1 (daoshu s2)))))

tests

(define sine-series (cons-stream 0 (integrate-series cosine-series)))
(define cosine-series (cons-stream 1 (integrate-series (stream-map (lambda (x) (* x -1)) sine-series))))
(define (add-streams s1 s2)(stream-map + s1 s2))

(define (integrate-series stm)
    (define (inner s a)
        (cons-stream (* (/ 1 a) (stream-car s)) 
                     (inner (stream-cdr s) (+ a 1))))
    (inner stm 1))

(define tan-series (div-series sine-series cosine-series))
(stream-head tan-series 10)

;Value 13: (0 1 0 1/3 0 2/15 0 17/315 0 62/2835)
;It's correct.

  
  
  
  
  
 (define (div-series stream1 stream2) 
     (let ((s2-car (stream-car stream2))) 
         (if (= s2-car 0) 
             (error "Denominator constant term cannot be 0 ！-- DIV-SERIES" s2-car) 
             (let ((reciprocal-s2-car (/ 1 s2-car))) 
                 (mul-series 
                     (scale-stream stream1 reciprocal-s2-car) 
                     (reciprocal-series (scale-stream stream2 reciprocal-s2-car))))))) 
  
 (define tangent-series (div-series sine-series cosine-series))