Modules

36b5c65c-ecea-429c-9f3d-a46b9c4d30ce 15 6 9 decimal

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

1. Universal algo style

Collapse  "Dichotomy"  in  "Utilities" # Ω a b ε roots RootDichotomy xn b a + (2 / : n 0 : xn Ω abs ε > xn Ω a Ω * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 51 line :

Collapse  "ExtremaDichotomy"  in  "Utilities" # Φ a b ε Extr ExtremaDichotomy x D x Φ x diff : xn b a + (2 / : n 0 : xn D abs ε > xn D a D * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 61 line :

x f 21 x 3^+ (* - x 2^7 - x 2^+ (* + :

x D1 x f x diff :

roots of the function x f 2 - 1 - 1012 -^roots x f 341012 -^roots 21 mat 1.92251847331763 - 3.85215343032542 21 mat

2. Pre-defined algo style

Local extrema of the function x f 2 - 1 - 1012 -^Extr x f 1 - 11012 -^Extr x f 241012 -^Extr 31 mat 1.26556443707467 - 0 2.76556443707464 31 mat

Collapse  "Dichotomy"  in  "Utilities" Φ a b ε D RootDichotomy xn b a + (2 / : n 0 : xn Φ abs ε > xn Φ a Φ * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 51 line :

x f x D1 2 1 sys

x f x 2^2 x * - 5 - :

ε 1013 -^:

x datum π :

x Φ x f :

R x f 1 - 2 - ε D x f 34 ε D 21 mat : 1.44948974278316 - 3.44948974278317 21 mat

x f 1.45 - 0 + 15 red 3.45 0 + 15 red 2 5 mat 2 1 sys

Sanity check R 1 el f R 2 el f 21 mat 7.4 1014 -^* - 3.2 1014 -^* - 21 mat

Modules

A robust construct of the Scale function M Low High Scale min M Min : max M Max : maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 61 line :

f γ M fmap i 1 M rows range j 1 M cols range V i j el M i j el f Re eval : for for ---next: Gamma scaling--- min V Min : max V Max : 12 mat i 1 V rows range j 1 V cols range V i j el V i j el min - max min - / γ * Floor eval : for for V 51 line :

Generate the symmetric square [U,V] matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx i * dx - (+ : for U 41 line :

t0 1 time :

a 816 π * sqrt * :

L 10 - : H 10 : N 50 : 13 mat

x y Φ 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - :

U L H N xd :

V U :

M x y Φ U V Sym 0255 Scale :

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M M :

Grayscale Image: Vectorise, scale γ

v M 25 row transpose :

v x el

A 1 : xo 128 : n 0.125 : 31 line

x f A x xo - (n^abs * : pγ f 255 M fmap : 21 line

U 02551 range : i 1 U rows range N i el U i el f : for Ω U N augment : 31 line

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1 time t0 - 50 sec *

hatch(f,g,x1,x2,N)

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x1 x2 N hatch dx x2 x1 - N / (: h x1 x1 f x1 x1 g 22 mat : x x1 x2 dx - x1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x f 1 x / :

x g 0 :

b 3 :

H x f x g 1 b 10 hatch :

Classroom hatch demo ln(x)

x f x g H 3 1 sys

x f x 1 b int 1.098612

b ln 1.098612