Daniel-Nikpayuk_SICP-Solutions/Chapter 1/1.3/exercise-1.40 (newtons-method)/exercise.lsp
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;; 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 tolerance 0.00001)

(define (fixed-point f first-guess)
 (define (close-enough? v1 v2)
  (< (abs (- v1 v2)) tolerance)
 )
 (define (try guess)
  (let ((next (f guess)))
   (display next)
   (newline)
   (if (close-enough? guess next)
       next
       (try next)
   )
  )
 )
 (try first-guess)
)

(define (deriv g)
  (lambda (x)
    (/ (- (g (+ x dx)) (g x))
       dx)))

(define dx 0.00001)

(define (newton-transform g)
  (lambda (x)
    (- x (/ (g x) ((deriv g) x)))))
(define (newtons-method g guess)
  (fixed-point (newton-transform g) guess))

(define (cubic a b c)
 (lambda (x) (+ (* x x x) (* a x x) (* b x) c))
)

(display "1.40")
(newline)
(display (newtons-method (cubic 1 1 1) 1))

