Daniel-Nikpayuk_SICP-Solutions/Chapter 3/3.5/exercise-3.59 (power-series integration)/exercise.lsp
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Copyright 2015 Daniel Nikpayuk
;;
;; This file is part of SICP Solutions.
;;
;; SICP Solutions is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License
;; as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
;;
;; SICP Solutions is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
;; of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License along with SICP Solutions. If not, see
;; <http://www.gnu.org/licenses/>.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(define integers (cons-stream 1 (add-streams ones integers)))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; a)

(define (integrate-series terms)
 (stream-map / terms integers)
)

;; b)

(define (additive-invert-series series)
 (if (stream-null? series) the-empty-stream
  (cons-stream (- (stream-car series)) (additive-invert-series (stream-cdr series)))
 )
)

(define exp-series (cons-stream 1 (integrate-series exp-series)))

(define cosine-series (cons-stream 1 (integrate-series (additive-invert-series sine-series))))
(define sine-series (cons-stream 0 (integrate-series cosine-series)))

