test(image): better latex test document (#1392)

Current test.tex page is poorly written and often contains mistakes
(e.g. missing backspace in front of greek letters). I have created a
page that is much more useful. It contains some of the most beautiful
math equations ever written. The file is validated: "pdflatex test.tex"
command produces valid (and nice looking) PDF document.

The document is also much longer - I have some issues with it in nvim
(partial latex rendering or rendering that works only if something major
is changed), so maybe it can help Folke to check the latex preview
functionality once again.

<img width="1019" alt="Screenshot 2025-02-23 at 11 13 48"
src="https://github.com/user-attachments/assets/306715be-89c0-4186-8910-c0069717c23a"
/>

---------

Co-authored-by: Sasa Markovic <provincijalac@gmail.com>
This commit is contained in:
saxon1964 2025-02-27 08:46:07 +01:00 committed by GitHub
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4 changed files with 172 additions and 35 deletions

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.gitignore vendored
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@ -10,4 +10,5 @@ node_modules
tt.* tt.*
/tmp /tmp
repomix* repomix*
.DS_Store
.aider* .aider*

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\relax \relax
\gdef \@abspage@last{1} \@writefile{toc}{\contentsline {section}{\numberline {1}Image Tests}{1}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Test image centered in a figure environment.}}{1}{}\protected@file@percent }
\newlabel{fig:test_image}{{1}{1}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Some beautiful mathematical equations}{2}{}\protected@file@percent }
\gdef \@abspage@last{4}

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\documentclass{article} \documentclass{article}
\usepackage{graphicx} % For images \usepackage{graphics, amsmath, amssymb, multirow}
\usepackage{amsmath} % For math symbols \usepackage{geometry}
\usepackage{amssymb} % For extra math symbols \geometry{
\usepackage{multirow} % For extra math symbols a4paper,
total={170mm,257mm},
left=20mm,
top=20mm,
}
\begin{document} \begin{document}
\section{Image Tests} \section{Image Tests}
Inline image: Inline image: \includegraphics[width=0.15\textwidth]{test.png}
\includegraphics[width=0.5\textwidth]{test.png}
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -21,54 +23,184 @@ Inline image:
\newpage \newpage
\section{Some beautiful mathematical equations}
\section{Math Tests} Ramanujan's formula:
$$\frac{1}{\pi}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty\frac{(4k)! (1103+26390k)}{(k!)^4 396^{4k}}$$
$ Euler's formula: $e^{i\pi}+1=0$
cases(
E_x = E_0 e^(j omega t - y z),
H_y = gamma / (j omega mu_0) E_x = eta^e E_0 e^(j omega - y z) = H_0 e^(j omega t - y z)
)
$
Inline math: \(E=mc^2$ and $\int_0^1 x^2 \,dx\) Area of triangle with sides a,b,c is:
Inline math: $E=mc^2$ and $\int_0^1 x^2 \,dx$ $$A=\frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}$$
Displayed equation: The most important formula in calculus:
\[ \[
f(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!} f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}
\] \]
Equation environment: Einstain's field equations:
\[
R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}
\]
Gamma function:
\[
\Gamma(z) = \int_0^\infty t^{z-1} e^{-t} dt,\quad\Gamma(z+1) = z \Gamma(z)
\]
Pythagora's theorem:
$$a^2+b^2=c^2$$
Logarithms:
$$\log ab=\log a+\log b$$
Navier-Stokes equation:
$$\rho\left(\frac{\partial \textbf{v}}{\partial t}+\textbf{v}\cdot\nabla\textbf{v}\right)+\nabla p-\nabla\cdot\textbf{T}=\textbf{f}$$
Law of gravity:
$$F=G\frac{m_1m_2}{r^2}$$
Fourier transform:
\[
F(\omega) = \int_{-\infty}^\infty f(t) e^{-2\pi i t \omega} dt
\]
Maxwell's equations:
\begin{equation} \begin{equation}
a^2 + b^2 = c^2 \nabla \times \textbf{E}=\frac{\rho}{\epsilon_0}
\label{eq:pythagoras}
\end{equation} \end{equation}
Aligned equations: \begin{equation}
\nabla \cdot \textbf{H}=0
\end{equation}
\begin{align} \begin{equation}
x^2 + y^2 &= r^2 \\ \nabla \times \textbf{E}=-\frac 1c\frac{\partial \textbf{H}}{\partial t}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \end{equation}
\end{align}
\begin{equation}
\nabla \times \textbf{H}=\frac 1c\frac{\partial \textbf{E}}{\partial t}
\end{equation}
Schroedinger equation:
\[
i \hbar \frac{\partial \psi}{\partial t} = H\Psi
\]
Chaos theory:
$$x_{t+1}=kx_t(1-x_t)$$
Information theory:
\[
H=-\sum p(x)\log p(x)
\]
Black-Scholes equation:
$$\frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0$$
Second law or thermodynamics:
$$dS\ge 0$$
Mass-energy equivalence:
$$E=mc^2$$
Basel problem:
\[
\frac{\pi^2}{6}=\sum_{n=1}^\infty \frac{1}{n^2}
\]
Euler-Masceroni constant:
\[
\gamma = \lim_{n\to\infty}(\sum_{n=1}^\infty \frac{1}{n}-\log n)\approx 0.5772156649\ldots
\]
Binomial expansion:
\[
(a+b)^n = \sum_{k=0}^n \binom{n}{k} a^k b^{n-k}
\]
Gauss:
$$\int_{-\infty}^\infty e^{-x^2} dx = \sqrt{\pi}$$
The Callan-Symanzik equation:
\[
\left[M\frac{\partial}{\partial M}+\beta(g)\frac{\partial}{\partial g}+n\gamma\right]G^n(x_1,x_2,...,x_n;M,g)=0
\]
Minimal surface equation:
$$\mathcal{A}(u)=\int_\Omega(1+|\nabla u|^2)^{1/2} dx_1 dx_2 ... dx_n$$
Multiline equations: Multiline equations:
\begin{multline} \begin{eqnarray*}
a + b + c + d + e + f + g + h + i + j + k = \\ \cos{2\theta} & = & \cos^2\theta - \sin^2\theta \\
l + m + n + o + p + q + r + s + t + u + v & = & 2\cos^2\theta - 1 \\
\end{multline} & = & 1 - 2\sin^2\theta
\end{eqnarray*}
\newpage And finally:
\section{Testing Referencing} $$1=0.999999999999999999\ldots$$
Referencing an equation: See Eq.~\ref{eq:pythagoras}. Just for fun: $6 + 9 + 6 \cdot 9 = 69$
Referencing an image: See Fig.~\ref{fig:test_image}. Quadratic equation:
\[
ax^2+bx+c=0 \implies x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\]
Four more ways to calculate pi:
\begin{equation*}
\pi=\sum_{k=0}^\infty\left[\frac{1}{16^k}\left(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6} \right) \right]
\end{equation*}
\begin{equation*}
\frac{2}{\pi}=\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{2+\sqrt{2}}}{2}\cdot\frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}\cdot\ldots
\end{equation*}
\begin{equation*}
\pi = 3+\textstyle \cfrac{1}{7+\textstyle \cfrac{1}{15+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{292+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{1+\ddots}}}}}}}
\end{equation*}
Chudnovsky Formula:
\[
\frac{1}{\pi} = \frac{\sqrt{10005}}{4270934400} \sum_{k=0}^\infty \frac{(6k)! (13591409 + 545140134k)}{(3k)!\,k!^3 (-640320)^{3k}}
\]
Cauchy's integral formula:
$$f(a)=\frac{1}{2\pi i}\int_{C} \frac{f(z)}{z-a} dz $$
Stirling's factorial approximation:
$$n! = \sqrt{2 \pi n} \left( \frac{n}{e} \right)^n \left( 1 + O \left( \frac{1}{n} \right) \right)$$
\end{document} \end{document}