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 <[email protected]>

.gitignore

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

tests/image/test.aux

@@ -1,2 +1,6 @@
 \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}

tests/image/test.tex

@@ -1,16 +1,18 @@
 \documentclass{article}
-\usepackage{graphicx}  % For images
-\usepackage{amsmath}  % For math symbols
-\usepackage{amssymb}  % For extra math symbols
-\usepackage{multirow}  % For extra math symbols
+\usepackage{graphics, amsmath, amssymb, multirow}
+\usepackage{geometry} 
+\geometry{
+  a4paper,
+  total={170mm,257mm},
+  left=20mm,
+  top=20mm,
+}
 
 \begin{document}
 
 \section{Image Tests}
 
-Inline image:
-
-\includegraphics[width=0.5\textwidth]{test.png}
+Inline image: \includegraphics[width=0.15\textwidth]{test.png}
 
 \begin{figure}[h]
     \centering
@@ -21,54 +23,184 @@ \section{Image Tests}
 
 \newpage
 
+\section{Some beautiful mathematical equations}
+
+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: $e^{i\pi}+1=0$
+
+Area of triangle with sides a,b,c is: 
+
+$$A=\frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}$$
+
+The most important formula in calculus:
+
+\[
+  f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}
+\]
+
+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: 
 
-\section{Math Tests}
+$$\log ab=\log a+\log b$$
 
+Navier-Stokes equation:
 
-$
-  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)
- )
-$
+$$\rho\left(\frac{\partial \textbf{v}}{\partial t}+\textbf{v}\cdot\nabla\textbf{v}\right)+\nabla p-\nabla\cdot\textbf{T}=\textbf{f}$$
 
-Inline math: \(E=mc^2$ and $\int_0^1 x^2 \,dx\)
+Law of gravity:
 
-Inline math: $E=mc^2$ and $\int_0^1 x^2 \,dx$
+$$F=G\frac{m_1m_2}{r^2}$$
 
-Displayed equation:
+Fourier transform:
 
 \[
-    f(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}
+  F(\omega) = \int_{-\infty}^\infty f(t) e^{-2\pi i t \omega} dt
 \]
 
-Equation environment:
+Maxwell's equations: 
 
 \begin{equation}
-    a^2 + b^2 = c^2
-    \label{eq:pythagoras}
+\nabla \times \textbf{E}=\frac{\rho}{\epsilon_0}
 \end{equation}
 
-Aligned equations:
+\begin{equation}
+\nabla \cdot \textbf{H}=0
+\end{equation}
+
+\begin{equation}
+\nabla \times \textbf{E}=-\frac 1c\frac{\partial \textbf{H}}{\partial t}
+\end{equation}
+
+\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:
+
+$$\frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0$$
 
-\begin{align}
-    x^2 + y^2 &= r^2 \\
-    \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0}
-\end{align}
+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:
 
-\begin{multline}
-    a + b + c + d + e + f + g + h + i + j + k = \\
-    l + m + n + o + p + q + r + s + t + u + v
-\end{multline}
+\begin{eqnarray*}
+\cos{2\theta} & = & \cos^2\theta - \sin^2\theta \\
+              & = & 2\cos^2\theta - 1 \\
+              & = & 1 - 2\sin^2\theta
+\end{eqnarray*}
 
-\newpage
+And finally:
+
+$$1=0.999999999999999999\ldots$$
+
+Just for fun: $6 + 9 + 6 \cdot 9 = 69$
+
+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*}
 
-\section{Testing Referencing}
+\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*}
 
-Referencing an equation: See Eq.~\ref{eq:pythagoras}.
+\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*}
 
-Referencing an image: See Fig.~\ref{fig:test_image}.
+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}
+
+
+
+