From 07f4b9adff7af45a7e0eb22d85a422e32ed4b1ca Mon Sep 17 00:00:00 2001 From: saxon1964 <71132278+saxon1964@users.noreply.github.com> Date: Thu, 27 Feb 2025 08:46:07 +0100 Subject: [PATCH] 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. Screenshot 2025-02-23 at 11 13 48 --------- Co-authored-by: Sasa Markovic --- .gitignore | 1 + tests/image/test.aux | 6 +- tests/image/test.pdf | Bin 60003 -> 7924555 bytes tests/image/test.tex | 200 +++++++++++++++++++++++++++++++++++-------- 4 files changed, 172 insertions(+), 35 deletions(-) diff --git a/.gitignore b/.gitignore index c570bb57..84d2b4c0 100644 --- a/.gitignore +++ b/.gitignore @@ -10,4 +10,5 @@ node_modules tt.* /tmp repomix* +.DS_Store .aider* diff --git a/tests/image/test.aux b/tests/image/test.aux index b6401217..38ddcc6a 100644 --- a/tests/image/test.aux +++ b/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} diff --git a/tests/image/test.pdf b/tests/image/test.pdf index a3c88743c5da19c6c3db762d4ff864da37e1e428..28a08ad8f29bf13e7cb315256ac686cb9f985da7 100644 GIT binary patch literal 7924555 zcmZs?Wl$Vk&@M;_!QI`0BsdK24#C}ZaCZiG4GuvDcNshccXtWy?i$>geZPBmx9(Q$ z`PHYZt4~)y{pUR0O{*d)&CJfig-km$Ke&v{Ny$d(1hhpK6hvlKuyC|;x2ELa<)!@J z2bopc#@^k+m6BE3-qhVf(!$Ki+yYrx7}?F;)xy*P*=sd5Nl3Y$4Kw2L?I%f2Z~FT4 zZbCes1_Oy2w@LY`iWGH)EJ`qvm(8veqR7p2(Ov;zOgp+YqHY`erb zQQr^(sS>(f>5ItzR>nq`INNbbNc(2Zf&Qz;#j-??$qJn$S{oM4PWEO3#d`*Ds9YF} z`@6be)0e?nV#Fv?SH$g%I&{?Gf+war%j?$NCD*Q9(d?qde?A5m2qBU3*QCQ_v5Vd_ z27rjC7F0Uhj?wMcn?MuAb9P>WKsoZ!sbh!V&%G`EnR$bPyk8|P)RQ5Y(UTh>R>vlqo` zc<{6t!ua;fV;tGS(ft2T)qm3eq?!HyNVkT!vjruqjxx~J!pt3+Row&V{=YOo989e& zkXf~D%>M@rK6VadR#^)hD{FU3c5c9b7jYYRHx&z42`2|GlRtYD2Cs%c6 zQ?vg(N?Lf@m|3XFi2uKc^6>ES@N%>NKXCqk(EQK*e^6C1b#-tP6#U!JYkD|z4e+T`s)O96@`k)5p-Ga| zKj|}N%V#*kkquXT$*bDCZ`kT=gsq=1;dnmpM={UF}lSVX2sW(kkQ z?x8)M(HWM?j*iM=IncL{P7Sai#NzuTiHaa5b~+_)67L9?Xp?({1;@d$L=ErCEC*8~ zDZ3TCp0iD)S&6nx1b+*~QZM|h#^cI{DCz9V8=C

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z)d@d_SmK+wuWx)TQ~>n5Z#8fEW0`y|*fvv-!WUX-UE5u)7|NYGRS&-Th_`S=zPM)Z wuzj8+Wcd1hD~3hNRr)cuL)$eL26+Uf34&=KMn@nd3VPBHfBjlPQxWgK0DnU~ZvX%Q diff --git a/tests/image/test.tex b/tests/image/test.tex index 7f9ca2f3..dda1104e 100644 --- a/tests/image/test.tex +++ b/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 @@ Inline image: \newpage +\section{Some beautiful mathematical equations} -\section{Math Tests} +Ramanujan's formula: +$$\frac{1}{\pi}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty\frac{(4k)! (1103+26390k)}{(k!)^4 396^{4k}}$$ -$ - 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) - ) -$ +Euler's formula: $e^{i\pi}+1=0$ -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} - 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{align} - x^2 + y^2 &= r^2 \\ - \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} -\end{align} +\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: + +$$\frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0$$ + +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: -\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} + + + +

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