From 8d11c6c8213f46f0fa19826917c255edd5d43cb1 Mon Sep 17 00:00:00 2001
From: mzuenni <mzuenni@users.noreply.github.com>
Date: Sun, 28 Jul 2024 22:54:40 +0200
Subject: Test (#4)

* update

* moved content in subdir

* rename file

* add test setup

* add test setup

* add github action

* automaticly test all cpp files

* timeout after 10s

* setulimit and dont zero memory

* test build pdf

* install latexmk

* update

* update

* ngerman

* fonts

* removed old code

* add first test

* added tests

* test in sorted order

* more tests

* simplified test

* more tests

* fix suffix tree

* fixes and improvements

* done ust lst directly

* fix swap

* add links to pdf

* fix constants

* add primorial

* add comment

* various improvements

* more tests

* added missing stuf

* more tests

* fix tests

* more tests

* more tests

* more tests

* fix recursion?

* test trie

* more tests

* only use python temporarily for listings

* only use python temporarily for listings

* more tests

* fix longestCommonSubstring

* more tests

* more tests

* made code more similiar

* fix?

* more tests

* more tests

* more tests

* add ahoCorasick test + limit 4GB stack size

* more tests

* fix test

* add additional test

* more tests

* more tests

* fix?

* better fix

* fix virtual tree

* more tests

* more tests

* recursive closest pair

* more tests

* decrease limit

* new tests

* more tests

* fix name

* more tests

* add test

* new test

* more tests

* more tests

* more tests

* more tests

* new test and content

* new code

* new code

* larger tests

* fix and test

* new test

* new test

* update pdf

* remove comments

* new test

* more tests

* more testcases

* more tests

* increased limit

* more tests

* more tests

* more tests

* new tests

* more tests

* shortened code

* new test

* add basic tests for bigint

* more tests

* removed old files

* new test

* ignore some files

* more auto more ccw

* fix test

* more tests

* fix

* new tests

* more tests

* more tests

* stronger test

* actually verify delaunay...

* more tests

* fix header

* more tests

* run tests parallel?

* test parralel?

* add --missing

* separate workflows

* test

* is the pdf checked?

* separate workflows

* fix workflow

* more workflows

---------

Co-authored-by: Yidi <noob999noob999@gmail.com>
---
 content/math/tables/numbers.tex | 59 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 content/math/tables/numbers.tex

(limited to 'content/math/tables/numbers.tex')

diff --git a/content/math/tables/numbers.tex b/content/math/tables/numbers.tex
new file mode 100644
index 0000000..1dc9f38
--- /dev/null
+++ b/content/math/tables/numbers.tex
@@ -0,0 +1,59 @@
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|l|X|}
+	\hline
+	\multicolumn{2}{|c|}{Berühmte Zahlen} \\
+	\hline
+	\textsc{Fibonacci}	&
+	$f(0) = 0 \quad
+	f(1) = 1 \quad
+	f(n+2) = f(n+1) + f(n)$ \\
+	\grayhline
+	
+	\textsc{Catalan}	&
+	$C_0 = 1 \qquad
+	C_n = \sum\limits_{k = 0}^{n - 1} C_kC_{n - 1 - k} =
+	\frac{1}{n + 1}\binom{2n}{n} = \frac{2(2n - 1)}{n+1} \cdot C_{n-1}$ \\
+	\grayhline
+	
+	\textsc{Euler} I &
+	$\eulerI{n}{0} = \eulerI{n}{n-1} = 1 \qquad
+	\eulerI{n}{k} = (k+1) \eulerI{n-1}{k} + (n-k) \eulerI{n-1}{k-1} $ \\
+	\grayhline
+	
+	\textsc{Euler} II &
+	$\eulerII{n}{0} = 1 \quad
+	\eulerII{n}{n} = 0 \quad$\\
+	& $\eulerII{n}{k} = (k+1) \eulerII{n-1}{k} + (2n-k-1) \eulerII{n-1}{k-1}$ \\
+	\grayhline
+	
+	\textsc{Stirling} I &
+	$\stirlingI{0}{0} = 1 \qquad
+	\stirlingI{n}{0} = \stirlingI{0}{n} = 0 \qquad
+	\stirlingI{n}{k} = \stirlingI{n-1}{k-1} + (n-1) \stirlingI{n-1}{k}$ \\
+	\grayhline
+	
+	\textsc{Stirling} II &
+	$\stirlingII{n}{1} = \stirlingII{n}{n} = 1 \qquad
+	\stirlingII{n}{k} = k \stirlingII{n-1}{k} + \stirlingII{n-1}{k-1} =
+	\frac{1}{k!} \sum\limits_{j=0}^{k} (-1)^{k-j}\binom{k}{j}j^n$\\
+	\grayhline
+	
+	\textsc{Bell} &
+	$B_1 = 1 \qquad
+	B_n = \sum\limits_{k = 0}^{n - 1} B_k\binom{n-1}{k}
+	= \sum\limits_{k = 0}^{n}\stirlingII{n}{k}$\\
+	\grayhline
+	
+	\textsc{Partitions} &
+	$p(0,0) = 1 \quad
+	p(n,k) = 0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0$ \\
+	& $p(n,k) = p(n-k,k) + p(n-1,k-1)$\\
+	\grayhline
+	
+	\textsc{Partitions} &
+	$f(0) = 1 \quad f(n) = 0~(n < 0)$ \\
+	& $f(n)=\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k+1)}{2})+\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k-1)}{2})$\\
+	
+	\hline
+\end{tabularx}
+\end{expandtable}
-- 
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