1 (defvar *tolerance* 0.0001)
2 (defun fixed-point (f first-guess)
3   (labels (
4 	   (close-enough? (v1 v2)
5 			  (< (abs (- v1 v2)) *tolerance*))
6 	   (try (guess)
7 		(let ((next (funcall f guess)))
8 		  (if (close-enough? guess next)
9 		      next
10 		    (try next)))))
11 	  (try first-guess)))
12 (defvar *dx* 0.00001)
13 (defun deriv (g)
14   (lambda (x)
15     (/ (- (funcall g (+ x *dx*))
16 	  (funcall g x))
17        *dx*)))
18 (defun newton-transform (g)
19   (lambda (x)
20     (- x (/ (funcall g x)
21 	    (funcall (deriv g) x)))))
22 (defun newtons-method (g guess)
23   (fixed-point (newton-transform g) guess))
24 
25 (defun cubic (a b c)
26   (lambda (x)
27     (+ (cube x)
28        (* a (square x))
29        (* b x)
30        c)))