Skip to content

Commit

Permalink
putz with 2.41
Browse files Browse the repository at this point in the history
  • Loading branch information
Joseph Williamson committed Jan 11, 2018
1 parent fc91626 commit 7f9838d
Show file tree
Hide file tree
Showing 11 changed files with 7,739 additions and 114 deletions.
20 changes: 20 additions & 0 deletions 1.37-cont-frac.bak
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,20 @@
#lang racket


(define (cont-frac n d k)
(if (= k 0)
(/ (n k) (d k))
(+ (d k) (/ (n k)
(cont-frac n d (- k 1))))))

(define (cont-frac-iter n d k)
(define (iter n d k a)
(if (= k 0)
a
;(/ a (/ (n k)(/ (d k))))
(iter n d (- k 1) (+ (d k)(/ (n k)(/(n k)(d k)))))))
(iter n d k 0))

(cont-frac-iter (lambda (i) 1.0)
(lambda (i) 1.0)
1)
3 changes: 3 additions & 0 deletions 1.38-euler.txt
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
1/(1+1/(2+1/(1+1/(1+1/(4+1/(1+1/1)
2
1
365 changes: 365 additions & 0 deletions 1.40.bak
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,365 @@
#lang racket

(define (inc x)
(+ x 1))

(define (average x y)
(/ (+ x y) 2))

(define (square x)(* x x))

(define (cube x) (* x x x))

(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)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))


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


((average-damp square)5) ;15

;(define (sqrt x)
; (fixed-point
; (average-damp
; (lambda (y) (/ x y)))
; 1.0))

(define (cube-root x)
(fixed-point
(average-damp
(lambda (y)(/ x y)))
1.0));<-1st guess

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

(define dx 0.00001)

((deriv cube) 5)

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

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

(define (sqrt x)
(newtons-method
(lambda (y)
(- (square y) x))
1.0))

(define (fixed-point-of-transform
g transform guess)
(fixed-point (transform g) guess))

(define (sqrt-ad x)
(fixed-point-of-transform
(lambda (y) (/ x y))
average-damp
1.0))

(display "avg damp: ")
(sqrt-ad 19083)

(define (sqrt-nt x)
(fixed-point-of-transform
(lambda (y) (- (square y) x))
newton-transform
1.0))
(display "newton: ")
(sqrt-nt 19083)

(define (cubic a b c)
(lambda(x)
(+ (cube x)
(* a (square x))
(* b x)
c)))
(newtons-method(cubic 3 3 3) 1)

(define zero -2.259921049894855)
;check
((cubic 3 3 3) zero)

(define double
(λ(f)(λ(x)(f (f x)))))

(((double (double double)) inc) 5);21

(define compose
(λ (f g)
(λ (x)
(f (g x)))))

(define repeated1
(λ (f n)
(λ (x)
(define repeat
(λ(a)(+ a a)))
(repeat x))))


((compose square(compose square (λ(x)x)))5)

(((λ (f)
(compose f(compose f (λ(x)x))))square)5)

(((λ (f n)
(if(= n 0)
(compose f (λ(x)x))
"ELSE"))
square 0)
5)

(define (sub1 n)
(- n 1))

(sub1 234)
;works

(define (repeated f n)
(cond((= n 0)(λ(x)x))
((even? n)(repeated(compose f f)(/ n 2)))
(else(compose f (repeated f (- n 1))))))

;(repeated square 1)5)
;((repeated square 2)5)

(define (smooth f)
(lambda (x)
(/ (+ (f x)
(f (+ x dx))
(f (- x dx)))
3)))

(define (n-fold-smooth f n)
((repeated smooth n) f))

(((repeated smooth 16)square)2)












;(((double (λ(x)(double (double x)))) inc) 5);21

;(((λ(x)
; ((λ(x)(double(double x)))
; ((λ(x)(double(double x))) x)))
; inc)
; 5);21
;
;(((λ(x0)
; ((λ(x2)(double(double x2)))
; ((λ(x1)(double(double x1))) x0)))
; inc)
; 5);21
;
;(((λ(x2)(double(double x2)))
; ((λ(x1)(double(double x1))) inc))
; 5);21
;
;(((λ(x2)(double(double x2)))(double(double inc))) 5);21
;
;(((λ(x2)(double(double x2)))(double(λ (x)(inc(inc x))))) 5);21
;
;(((λ(x2)(double(double x2)))
; (λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))) 5);21
;
;((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))5)
;
;(λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))
;;is equivalent to
;((λ (x) (inc(inc(inc(inc x)))))5)
;
;((double(double (λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))))
; 5);21
;
;((double(λ (x)((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x))) x))))
; 5);21
;
;((double(λ (x)((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))
; ((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x))) x))))
; 5);21
;
;((λ (x)((λ (x)((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))
; ((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x))) x))) ((λ (x)((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x)))
; ((λ (x)((λ (x)(inc(inc x)))
; ((λ (x)(inc(inc x)))
; x))) x))) x)))5)
;
;
;
;((double inc)5) ;7
;
;(((double double)inc)5);9
;
;(((double (double double)) inc) 5);21
;
; (((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; ((lambda(f2)(lambda(x2)(f2 (f2 x2)))) inc))5)
; (display "should be 9: ")((lambda(x2)((lambda(x2)(inc (inc x2))) ((lambda(x2)(inc (inc x2))) x2)))5)
;((lambda(x2)(inc (inc x2))) ((lambda(x2)(inc (inc x2))) 5))
;;omg this sucks but it works
;((lambda(x2)(inc (inc x2))) (inc (inc 5)))
;
;(((lambda(x1)
; ((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; ((lambda(f2)(lambda(x2)(f2 (f2 x2)))) x1)))
;
; ((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; ((lambda(f2)(lambda(x2)(f2 (f2 x2)))) inc)))5)
;
;(((lambda(x1)
; ((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; ((lambda(f2)(lambda(x2)(f2 (f2 x2)))) x1)))
;
; ((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; (lambda(x2)( inc ( inc x2)))))5)
;
;(((lambda(f2)(lambda(x2)(f2 (f2 x2))))
; (lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2))))5)
;((lambda(x2)
; ((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2))) x2)))
;
;5)
;
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2))) 5))
;
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) 5)))
;
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) 5))))
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)( inc ( inc x2)))
; ( inc ( inc 5)))))
;
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)( inc ( inc x2)))
; 7)))
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ( inc ( inc 7))))
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; 9))
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; ((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) 9)))
;
;((lambda(x2)((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) x2)))
;
; 13)
;((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; ((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2))) 13))
;
;((lambda(x2)((lambda(x2)( inc ( inc x2)))
; ((lambda(x2)( inc ( inc x2))) x2)))
; 17)
Loading

0 comments on commit 7f9838d

Please sign in to comment.