(load "streams.txt")


; s1 = a1 + s1r*x
; s2 = a2 + s2r*x
; s1 * s2 = a1*a2 + a1*s2r*x + a2*s1r*x  + (s1r*x * s2r*x)
; = a1*a2 + x*(a1*s2r + a2*s1r  + (s1r * s2r)x)

(define (mul-series2 s1 s2)
  (let ((a1 (stream-car s1))
        (a2 (stream-car s2))
        (s1r (stream-cdr s1))
        (s2r (stream-cdr s2)))
    (cons-stream
      (* a1 a2)
      (add-streams
        (add-streams (scale-stream s2r a1) (scale-stream s1r a2))
        (cons-stream 0
			(mul-series2 s1r s2r))))))

; s1 = a1 + s1r*x
; s2 = a2 + s2r*x
; s1 * s2 = a1*a2 + a1*s2r*x + a2*s1r*x  + (s1r*x * s2r*x)
;         = a1*a2 + x(a1*s2r + a2*s1r  + s1r*s2r*x)
;         = a1*a2 + x((a1 + s1r*x)*sr2 + a2*s1r)
;         = a1*a2 + x(s1*sr2 + a2*s1r)

(define (mul-series s1 s2)
  (cons-stream
    (* (stream-car s1) (stream-car s2))
    (add-streams (scale-stream (stream-cdr s1) (stream-car s2))
                 (mul-series s1 (stream-cdr s2)))))

; 1 ]=> (load "3.59.txt")
; 
; ;Loading "3.59.txt"... done
; ;Value: sine-series
; 
; 1 ]=> (stream-prefix (add-streams (mul-series sine-series sine-series)
;                                   (mul-series cosine-series cosine-series)) 10)
; 
; ;Value: (1 0 0 0 0 0 0 0 0 0)