\documentclass[12pt]{article}
\usepackage{amsmath, amssymb}
\usepackage[margin=1in]{geometry}
\title{Fourier Analysis}
\author{A. Mercier}
\date{\today}
\begin{document}
\maketitle
\section{Transform Definition}
The Fourier transform of $f(t)$ is:
\[
\hat{f}(\xi) = \int_{-\infty}^{\infty}
f(t)\, e^{-2\pi i \xi t}\, dt
\]
\section{Parseval's Theorem}
For square-integrable functions:
\[ \int_{-\infty}^{\infty} |f(t)|^2\, dt
= \int_{-\infty}^{\infty} |\hat{f}(\xi)|^2\, d\xi \]
\end{document}
\documentclass{article}
\usepackage{fontspec}
\usepackage{polyglossia}
\setmainlanguage{english}
\setotherlanguage{arabic}
\setmainfont{Noto Serif}
\newfontfamily\arabicfont[Script=Arabic]{Noto Naskh Arabic}
\begin{document}
\section{Multilingual Typesetting}
XeLaTeX handles Unicode natively, enabling seamless
mixing of scripts and writing systems.
\begin{Arabic}
مرحباً بالعالم — Arabic renders right-to-left.
\end{Arabic}
Custom OpenType features and any system font are
available via the \texttt{fontspec} package.
\end{document}
\documentclass{article}
\usepackage{luacode, booktabs}
\begin{document}
\section{Dynamic Table via Lua}
\begin{luacode}
local rows = {
{"Product", "Q1", "Q2", "Q3" },
{"Alpha", "120", "145", "162"},
{"Beta", "98", "110", "134"},
{"Gamma", "55", "72", "89" },
}
tex.print("\\begin{tabular}{lrrr}")
tex.print("\\toprule")
for i, row in ipairs(rows) do
tex.print(table.concat(row, " & ") .. " \\\\")
if i == 1 then tex.print("\\midrule") end
end
tex.print("\\bottomrule")
tex.print("\\end{tabular}")
\end{luacode}
\end{document}
\documentclass{article}
\usepackage[backend=biber, style=apa]{biblatex}
\usepackage{hyperref}
\addbibresource{references.bib}
\begin{document}
\section{Introduction}
The work by~\cite{knuth1984} established the principles
of typographic quality that \LaTeX{} implements.
Later, \cite{lamport1994} formalized the macro layer
now universal in academic publishing.
\section{Results}
\label{sec:results}
Cross-references like \autoref{sec:results} resolve
correctly — latexmk reruns as many times as needed,
handling BibTeX, indices, and \texttt{hyperref} links.
\printbibliography
\end{document}
