239406b6-298d-4da6-be6c-0c413ac809f4 23 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

design/assign f(x) components externally

x f 2110 x - (* 260 x - 2 / 5128 x - (* 4 / 5128 x - (* 5100 0.5 x * + (* 2 / 51 mat min : x bound 1225 x - (* 10 / : x y axes x y / - : 31 sys

plot x f x bound 402004064 - 22 mat 8015080200 - 22 mat axes 51 sys :

plot

f(x)

plot

x f x bound - x 89.796 - 160.526 int 22322

x f x bound - 0 ≡ x 100 - 50 - solve x f x bound - 0 ≡ x 128200 solve 21 mat 89.796 - 160.526 21 mat

Dichotomy for solving in the complex region

x f 260 x - 2 / 5128 x - (* 4 / - :

a 0 : b 100 : xn b a + (2 / : 31 line

ε 106 -^:

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 40

x f 2110 x - (* 5128 x - (* 4 / - :

a 50 : b 100 : xn b a + (2 / : 31 line

xn f 4

ε 109 -^:

.. sanity ..

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

n 32

xn 80

xn f 0

h 0.01 :

x f 2110 x - (* 260 x - 2 / 5128 x - (* 4 / 5128 x - (* 5100 0.5 x * + (* 2 / 51 mat min :

n 32

Infinitesimal Derivative x h f deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* (:

x h f deriv

x f 2110 x - (* 260 x - 2 / 5128 x - (* 4 / 5128 x - (* 5100 0.5 x * + (* 2 / 51 mat min : x bound 1225 x - (* 10 / : 21 sys

x y1 x f : x y2 x bound : 21 sys

Filing the inscribed region

'N' random in critical region N 1000 :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

size/define critical region.
Plot first before filling xmin 501 - : xmax 200 : ymin 200 - : ymax 200 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

A function that tests an arbitrary point 
for its membership in the critical region. x y Test 1 y x y1 ≤ (* y x y2 ≥ (* :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

isolate  for X_Y Pts Pts :

#808080 midgray ≡

a b c spec . 6 #808080 13 mat : fill Pts a b c spec pts : 21 line

Filling a range of a critial domain

x f x bound fill 3 1 sys

x y axes x y / - :

x y1 x y2 Pts axes 4 1 sys