LaTeX Skill

This skill governs the production of LaTeX output for a researcher in computational and applied mathematics whose work spans numerical optimisation, deep learning theory, electrical impedance tomography (EIT), regularisation theory, data-driven inversion, numerical analysis, PINNs, and related areas. All output must satisfy the mathematical standards of journals such as SIAM Journal on Scientific Computing, Inverse Problems, Mathematics of Computation, and Journal of Computational Physics.

Step 1. Classify the Request

Before writing anything, determine which of the three output modes applies. Check for BEAMER MODE first, since it has the strongest surface signals.

Beamer Mode ← CHECK THIS FIRST

Produce a complete Beamer presentation (.tex file with \documentclass{beamer}) when the request contains any of:

The words "slides", "presentation", "beamer", "slide deck", "talk", "seminar", "conference talk", or "present my work on".
A request to prepare a talk from a manuscript, paper draft, or set of results.
A request for a "title slide", "table of contents slide", or named academic sections such as "introduction slide", "convergence results slide", "numerical experiments slide".

Proceed to Step 2B for the beamer preamble and Step 3B for beamer content rules. Do NOT use the article preamble (Step 2) or article document structure (Step 4) for Beamer Mode output.

Content sourcing for Beamer Mode:

If the user supplies a complete manuscript or paper: extract content from it faithfully to populate each slide section.
If the user supplies only a title, abstract, or partial notes: generate a fully structured template with \todo{} placeholders in every slide that lacks content.
Never fabricate theorems, lemmas, or numerical results that were not provided.

Document Mode

Produce a complete, standalone .tex file (preamble through \end{document}) using \documentclass{article} when the request involves:

A theorem, lemma, proposition, corollary, definition, or remark, with or without proof.
A multi-step derivation or mathematical argument.
A convergence analysis or complexity result.
An algorithm presented alongside its theoretical justification.
An introduction, related-work survey, or structured academic section.
A self-contained report, technical note, or preprint draft.

Save the output as a .tex file and present it to the user for download.

Snippet Mode

Produce raw LaTeX body content only (no \documentclass, no preamble, no \begin{document}) when the request involves:

A single equation or aligned system of equations.
An algorithm or pseudocode block in isolation.
A numerical results table.
A TikZ figure or pgfplots graph.
Any fragment intended to be inserted into the user's own template.

Deliver snippet output as a labelled code block in the chat, not as a file, unless the user explicitly requests a file.

When in doubt, ask: "Should I produce a complete standalone document, a snippet, or a Beamer presentation?"

Step 2. Apply the Standard Preamble (Document Mode Only)

Use the preamble below verbatim. Do not improvise or abbreviate it.

\documentclass[11pt,a4paper]{article}

% ---------------------------------------------------------------
% Core mathematics packages
% ---------------------------------------------------------------
\usepackage{amsmath, amssymb, amsthm, mathtools}
\usepackage{bm}            % bold math symbols
\usepackage{dsfont}        % indicator function \mathds{1}

% ---------------------------------------------------------------
% Algorithms
% ---------------------------------------------------------------
\usepackage[ruled,vlined,linesnumbered]{algorithm2e}

% ---------------------------------------------------------------
% Graphics, figures, and plots
% ---------------------------------------------------------------
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepackage{subfigure}     % side-by-side figures
\usepackage{adjustbox}     % fallback rescaling for wide TikZ diagrams

% ---------------------------------------------------------------
% Tables
% ---------------------------------------------------------------
\usepackage{booktabs}
\usepackage{tabularx}
\usepackage{siunitx}       % decimal-aligned columns, SI units

% ---------------------------------------------------------------
% Cross-referencing and citations
% ---------------------------------------------------------------
\usepackage[numbers,sort&compress]{natbib}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
\usepackage[capitalise,noabbrev]{cleveref}

% ---------------------------------------------------------------
% Typography
% ---------------------------------------------------------------
\usepackage{microtype}
\usepackage{parskip}
\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt}

% ---------------------------------------------------------------
% Page layout
% ---------------------------------------------------------------
\usepackage[margin=2.5cm]{geometry}

% ---------------------------------------------------------------
% Miscellaneous
% ---------------------------------------------------------------
\usepackage{xcolor}
\usepackage{todonotes}     % \todo{} markers for placeholders

% ---------------------------------------------------------------
% Theorem environments (amsthm)
% ---------------------------------------------------------------
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{assumption}{Assumption}
\newtheorem{example}[theorem]{Example}

\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}

% ---------------------------------------------------------------
% Notation macros (computational and applied mathematics)
% ---------------------------------------------------------------
% Norms and inner products
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\normF}[1]{\left\lVert #1 \right\rVert_{\mathrm{F}}}
\newcommand{\ip}[2]{\left\langle #1,\, #2 \right\rangle}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}

% Calculus and optimisation
\newcommand{\grad}{\nabla}
\newcommand{\Hess}{\nabla^2}
\newcommand{\Lapl}{\Delta}
\newcommand{\divergence}{\operatorname{div}}
\newcommand{\curl}{\operatorname{curl}}

% Function spaces
\newcommand{\Lp}[1]{L^{#1}}
\newcommand{\Sob}[2]{H^{#1}(#2)}
\newcommand{\SobZ}[2]{H^{#1}_0(#2)}

% Operators and matrices
\newcommand{\bA}{\mathbf{A}}
\newcommand{\bB}{\mathbf{B}}
\newcommand{\bJ}{\mathbf{J}}
\newcommand{\bK}{\mathbf{K}}
\newcommand{\bI}{\mathbf{I}}
\newcommand{\bx}{\mathbf{x}}
\newcommand{\by}{\mathbf{y}}
\newcommand{\bz}{\mathbf{z}}
\newcommand{\bu}{\mathbf{u}}
\newcommand{\bv}{\mathbf{v}}

% Probability and statistics
\newcommand{\E}{\mathbb{E}}
\newcommand{\Prob}{\mathbb{P}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\indicator}{\mathbf{1}}

% Asymptotic notation
\newcommand{\bigO}[1]{\mathcal{O}\!\left(#1\right)}
\newcommand{\smallO}[1]{o\!\left(#1\right)}

% Common domains
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\C}{\mathbb{C}}

% Regularisation (EIT / inverse problems)
\newcommand{\Reg}{\mathcal{R}}
\newcommand{\Forward}{\mathcal{F}}
\newcommand{\Tikhonov}[3]{\norm{#1 - #2}^2 + #3\,\Reg(#2)}

% Iterates and step sizes
\newcommand{\xk}{x_k}
\newcommand{\alphak}{\alpha_k}
\newcommand{\etak}{\eta_k}

Step 2B. Beamer Preamble (Beamer Mode Only)

Use the preamble below for ALL Beamer presentations. Do NOT mix with the article preamble in Step 2. The two preambles are mutually exclusive.

Theme selection: The default theme is Madrid. If the user specifies a di

latex