latex-textbook-writer

name	latex-textbook-writer
description	Use when writing math textbook content in XeLaTeX, including definitions, theorems, proofs, and section formatting in English or Chinese.

LaTeX Textbook Writer

Shared narrative rules

Read and follow the shared narrative and evidence rules. Apply the direct, reader-facing style when explaining mathematical content; do not add process-oriented or defensive source disclaimers to the textbook.

Professional assistant for writing mathematical textbooks using XeLaTeX with proper formatting, structure, and narrative style.

Overview

This Skill provides comprehensive guidance for writing mathematics textbooks with:

• Professional box styles (definitions, theorems, examples, remarks)
• Correct color scheme (definitions in green, theorems in orange, examples in blue)
• Academically standard narrative style (explanation before definition, interwoven narrative and boxes)
• English and Chinese template support

When to Use

Use this Skill when creating or modifying:

• Mathematics textbook chapters
• LaTeX formatting for theorems, definitions, proofs
• Professional styling for academic papers
• Projects requiring Chinese/English mathematical typesetting

Language Settings (Critical!)

When using ctex package for Chinese support, theorem names and figure captions automatically become Chinese. Always add these overrides for English documents:

\usepackage{ctex}
\usepackage{amsmath,amssymb,amsthm}
\renewcommand{\proofname}{Proof}         % Force English "Proof"
\renewcommand{\contentsname}{Contents}   % Force English "Contents"
\usepackage{caption}
\captionsetup{figurename=Figure,tablename=Table}  % Force English captions

Color Scheme

• Definitions/Notation: Green RGB(34,139,34)
• Theorems/Propositions/Lemmas/Corollaries/Proofs: Orange RGB(230,126,0)
• Chapter/Section Titles: Blue RGB(0,51,102)
• Examples: Blue RGB(70,130,180)
• Exercises: Brown RGB(139,69,19)
• Remarks: Gray RGB(200,200,200) (no border, no title)

Box Style Specifications

All theorem/definition/example boxes use \newtcbtheorem with:

• Title inside border (no separate boxed title bar for cleaner look)
• Title format: "2.2.1 Coin Flip Counting" (number, then title)
• Title font: Sans-serif bold white text on colored background
• Content font: Upright/roman (not italic)
• Padding: left=10pt, right=10pt, top=15pt, bottom=8pt
• Border: 1pt colored line with 6pt rounded corners
• Title spacing: toptitle=1mm, bottomtitle=1mm
• Syntax: \begin{definition}{Title}{label} (two arguments, not [Title])

Core Writing Principles

1. Narrative Flow (Most Important!)

NEVER start a section directly with a definition/theorem box. ALWAYS include explanatory text first.

BAD (boxes without introduction):

\section{Groups}
\begin{definition}{Group}{def:group}
...
\end{definition}

GOOD (narrative leads into boxes):

\section{Groups}
Group theory studies groups, the most fundamental algebraic structures. This section introduces the definition and basic properties of groups.

\begin{definition}{Group}{def:group}
A group is a set $G$ with a binary operation satisfying...
\end{definition}

The above definition requires three key conditions...

2. Narrative Should Weave Through Content

The goal is narrative-box-narrative-box-narrative, not narrative-box-box-box-narrative.

After a box, add:

• Explanatory text unpacking the result
• Connections to previous concepts
• Motivation for what comes next
• Physical or mathematical interpretation

3. Proofs as Coherent Narratives

Proofs should flow as continuous text, not step-by-step lists.

BAD:

\textbf{Step 1}: ...
\textbf{Step 2}: ...
\textbf{Step 3}: ...

GOOD:

\begin{proof}
Since $U \in SU(4)$ and the exponential map is surjective, there exists $X \in \mathfrak{su}(4)$ such that $\exp(X) = U$.

Next, we express $X$ as a linear combination of Hamiltonians. By the completeness of the Lie algebra...

Therefore, the theorem is proved. $\square$
\end{proof}

4. No Italics - Use Bold for Emphasis

DO NOT use italics in mathematical textbooks. Use bold for:

• Emphasis on important concepts
• Proper nouns (names of mathematicians, special terms)
• Key terms being introduced

BAD:

Let $V$ be a *vector space*. The \textit{Hahn-Banach theorem} states...

GOOD:

Let $V$ be a vector space. The \textbf{Hahn-Banach theorem} states...

Bold a term to introduce or name it; do not use vague emphasis words such as "核心", "关键", "重要", "主要", "本质", or "显著" as a substitute for saying what a concept is or does. State the definition, hypothesis, or measured effect directly.

5. Bulleted and Numbered Lists

ONLY use bullets (itemize) and numbered lists (enumerate) in:

• Example boxes (\begin{example}...\end{example})
• Exercise sections (\begin{exercise}...\end{exercise})

NEVER use bullets or numbered lists in main narrative text.

Reader-Relevance Filter

Keep only sentences that help the reader understand the mathematics: definitions, assumptions, relations, proofs, examples, consequences, or necessary limitations. Do not include meta-commentary about the author's writing process, intent, fidelity to a source, or why an omission was made. Do not explain that an unsupported point cannot be inferred merely to describe the drafting process; omit it or state the concrete mathematical limitation when it matters.

6. Chinese Quote Marks (CRITICAL for Chinese Documents!)

When writing Chinese text in LaTeX (with ctex package), ALWAYS use proper quote marks:

Chinese Double Quotes:

• Left double quote: `` (two backticks)
• Right double quote: '' (two single quotes/apostrophes)

Chinese Single Quotes:

• Left single quote: ` (one backtick)
• Right single quote: ' (one single quote/apostrophe)

How to type:

• Press backtick key (`) twice for left double quote: ``
• Press apostrophe key (') twice for right double quote: ''
• Press backtick key once for left single quote: `
• Press apostrophe key once for right single quote: '

Examples:

% CORRECT - Chinese quotes
The concept of ``closeness'' and ``continuity''...
This is a ``simple'' definition.

% INCORRECT - ASCII straight quotes (ugly in PDF)
The concept of "closeness" and "continuity"...

IMPORTANT: Always use and '' for quotes in Chinese text, never use ", corner brackets, or any other form!

7. Specify Variable Domains Before Formulas

ALWAYS state which set each variable belongs to before writing formulas, not after.

BAD (domain specified after formula):

We can verify
$$
\langle \operatorname{ad}_{X}(Y), Z \rangle = \langle Y, \operatorname{ad}_{X^{*}}(Z) \rangle
$$
for $X \in \mathfrak{r}$ and $Y, Z \in \mathfrak{g}$.

GOOD (domain specified first):

Take any $X \in \mathfrak{r}$ and $Y, Z \in \mathfrak{g}$. We can verify
$$
\langle \operatorname{ad}_{X}(Y), Z \rangle = \langle Y, \operatorname{ad}_{X^{*}}(Z) \rangle
$$

Use phrases like: "Take any...", "For...", "Let...", "For any...".

Box Title Format

English format:

• "1.22 Definition: Real Vector Space"
• "1.14 Commutativity of Addition in F^3"
• "1.10 Notation: n"
• "1.44 Example: A Sum That Is Not Direct"

Chinese format (for Chinese documents):

• "1.22 定义：实向量空间"
• "1.14 $F^3$ 中加法的可交换性"
• "1.10 记号：$n$"
• "1.44 例：一个不是直和的和"

Section Numbering Format

English:

• Chapter: "Chapter 1", "Chapter 2"
• Section: "1.1", "1.2", "2.1"
• Subsection: No numbering, just larger sans-serif blue font

Chinese:

• Chapter: "第1章", "第2章"
• Section: "1.1", "1.2", "2.1"
• Subsection: No numbering, just larger sans-serif blue font

Standard Patterns

Pattern 1: Narrative -> Definition -> Explanation

Introduce the concept with background and motivation.

\begin{definition}{Concept Name}{def:concept}
Formal definition.
\end{definition}

Explain the meaning and intuition behind the definition.

Pattern 2: Proposition -> Proof -> Consequence Narrative

Set up the context for the proposition.

\begin{proposition}{Proposition Name}{prop:name}
Statement.
\end{proposition}

\begin{proof}
Coherent proof narrative.
\end{proof}

Discuss the significance and applications.

Quality Checklist

Before considering content complete:

1. Every section has introductory text before the first box
2. Narrative weaves through boxes (not box-box-box stacking)
3. Proofs are coherent narratives, not step lists
4. No bullets or numbered lists in main narrative text (only in examples/exercises)
5. No italics - use bold for emphasis/proper nouns
6. All environments use new syntax: \begin{definition}{Title}{label} (not [Title])
7. All referenceable items have unique labels in second argument
8. All cross-references use \ref{}
9. For English documents: Added \renewcommand{\proofname}{Proof} and \captionsetup{figurename=Figure,tablename=Table}
10. For Chinese documents: All quotes use and '', NOT " or corner brackets
11. Variable domains specified BEFORE formulas, not after
12. For answers.tex: Each solution uses \textbf{解：} / \textbf{Solution:} with one formula per line format
13. For answers.tex: No paragraph contains multiple inline formulas - use display math for each formula
14. Document compiles without errors

Compilation

# Always compile TWICE for cross-references
xelatex -interaction=nonstopmode main.tex
xelatex -interaction=nonstopmode main.tex

Reference Files

• references/format-en.tex: English textbook template
• references/format-zh.tex: Chinese textbook template

These templates contain complete preamble setup, color definitions, and box styles ready to copy into your project.

Exercise and Answer Appendices

When a 习题/ directory exists, create exercise.tex and answers.tex appendix files. Solutions must use "one formula per line" (一行一公式) format with display math for each formula.

See references/exercise-format.md for complete format specifications, examples, anti-examples, and translation guide.

Figures and Illustrations

Figures can be created using TikZ code inline in chapter .tex files, or using Python scripts (matplotlib) stored in a figures/ directory.

TikZ Figures (inline in chapter files)

For mathematical diagrams (group-algebra relationships, commutative diagrams, etc.), use TikZ code directly in chapter .tex files:

\begin{center}
\begin{tikzpicture}[
    box/.style={draw, rounded corners=4pt, ...},
    ...
]
    \node[box] (A) at (0,0) {$SU(2)$};
    ...
    \draw[->, thick] (A) -- (B);
\end{tikzpicture}
\end{center}

Python Figures (external scripts)

For plots, curves, and complex illustrations, use Python scripts:

project/
├── figures/              # Python scripts and generated images
│   ├── draw_xxx.py       # matplotlib scripts
│   ├── xxx.png           # Generated images
│   └── ...

• Runtime: conda run -n py313 python figures/draw_xxx.py
• Save as PNG with dpi=200, bbox_inches='tight', facecolor='white'
• Include via \includegraphics[width=0.85\textwidth]{figures/xxx.png}

Environment Syntax Reference

New syntax (using \newtcbtheorem):

% Definition with label
\begin{definition}{Title}{def:label}
    Content here...
\end{definition}

% Theorem with label
\begin{theorem}{Title}{thm:label}
    Statement here...
\end{theorem}

% Example with label
\begin{example}{Title}{ex:label}
    Content here...
\end{example}

% Remark (different syntax, no label)
\begin{remark}[Optional Title]
    Content here...
\end{remark}

% Proof (inline style, no colon)
\begin{proof}
    Proof content here...
\end{proof}

Important notes:

• Two arguments: {Title}{label} instead of [Title]
• Second argument is required (use descriptive labels like def:vector_space)
• The box title shows "Number Title" (e.g., "2.2.1 Coin Flip Counting")
• Proof environment uses \quad (two spaces) instead of colon after "Proof"
• Remark environment still uses optional [Title] syntax (no label needed)