eharetea

Using scheme to compute derivatives and integrals.

Scheme, a rendition of Lisp, is a great language used for numerous applications, one being artificial intelligence.

Date Created:Saturday September 06th, 2008 10:37 AM
Date Modified:Friday October 31st, 2008 10:03 PM

(define average (lambda (x y) (/ (+ x y))))

(define (average-damp f)
  (lambda (x) (average x (f x)) )
)

(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
     (< (abs (- v1 v2)) 0.00001)
  )
  (define (try guess)
	 (let ((next (f guess)))
	    (if (close-enough? guess next)
		    next
			(try next)
		)
	  )
  )
  (try first-guess)
)

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

(define (newton-transform g dx) (lambda (x) (- x (/ (g x) ((deriv g dx) x)))))

(define (newtons-method g guess dx) (fixed-point (newton-transform g dx) guess))

(define pi (newtons-method sin 3.14 0.0001) )

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

(define test-cubic (newtons-method (cubic 1 2 4) 1 0.001))

(define summation 
  (lambda (func inc x b) 
    (if (> x b)
        0
        (+
		  (func x)
		  (summation func inc (inc x) b)
		)
    )
  )
)

(define dx (lambda (x) (+ x 1) ) )
(define identity (lambda (x) x) ) 


(define sum 
    (lambda (func x b dx) 
    (define inc-dx (lambda (x dx) (+ x dx) ) )
	(if (> x b)
        0
        (+
		  (func x)
		  (sum func (inc-dx x dx) b dx)
		)
    )
  )
)

(define product 
    (lambda (func x b dx) 
    (define inc-dx (lambda (x dx) (+ x dx) ) )
	(if (> x b)
        1
        (*
		  (func x)
		  (product func (inc-dx x dx) b dx)
		)
    )
  )
)

(define (factorial x)
   (product identity 1 x 1)
)

(define (integral f a b dx)
  (*
    (sum f (+ a (/ dx 2.0)) b dx)
	dx
  )
)

Scheme mathematics by Dan Lynch
is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License
Based on a work at www.3daet.com
Permissions beyond the scope of this license may be available at http://www.3daet.com