# Meta: Wiki Capabilities, TeX Math & Typography Reference ## 1. Mathematical Typography: KaTeX TeX Math Engine The wiki is equipped with a high-performance **KaTeX** client-side rendering engine. Mathematical formulas and scientific equations are written using standard LaTeX math syntax. ### Delimiters * **Display Equations (Block Math)**: Enclose in double dollar signs `$$ ... $$` on their own lines. Centered and formatted with full display geometry. * **Inline Equations**: Enclose in single dollar signs `$ ... $` directly within sentences. ### Core TeX Math Examples & Cheat Sheet #### 1. Fractions, Exponents & Powers ```latex $$\text{FREQ} = \frac{433,920,000}{24,000,000} \times 2^{16} = 1,184,883 = \mathbf{0x121473}$$ ``` $$\text{FREQ} = \frac{433,920,000}{24,000,000} \times 2^{16} = 1,184,883 = \mathbf{0x121473}$$ #### 2. Symbol Timing & Multi-Term Equations ```latex $$\text{Data Rate} = \frac{(256 + \text{DRATE-M}) \times 2^{\text{DRATE-E}}}{2^{28}} \times f_{\text{XOSC}} = \mathbf{3433.22\text{ baud}}$$ ``` $$\text{Data Rate} = \frac{(256 + \text{DRATE-M}) \times 2^{\text{DRATE-E}}}{2^{28}} \times f_{\text{XOSC}} = \mathbf{3433.22\text{ baud}}$$ #### 3. Signal Flow & Daisy-Chains ```latex $$\text{Red (Source: fc79)} \longrightarrow \text{Blue (1st Sink)} \longrightarrow \text{Green (2nd Sink)} \longrightarrow \text{Yellow (75}\Omega\text{ Terminated)}$$ ``` $$\text{Red (Source: fc79)} \longrightarrow \text{Blue (1st Sink)} \longrightarrow \text{Green (2nd Sink)} \longrightarrow \text{Yellow (75}\Omega\text{ Terminated)}$$ #### 4. Radicals, Integrals & Summations ```latex $$f(x) = \int_{-\infty}^{\infty} \hat{f}(\xi) e^{2\pi i \xi x} \text{ } d\xi \qquad \sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k} = (x + y)^n$$ ``` $$f(x) = \int_{-\infty}^{\infty} \hat{f}(\xi) e^{2\pi i \xi x} \text{ } d\xi \qquad \sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k} = (x + y)^n$$ #### 5. Matrices & Linear Systems ```latex $$\begin{pmatrix} y_1 \\ y_2 \end{pmatrix} = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}$$ ``` $$\begin{pmatrix} y_1 \\\\ y_2 \end{pmatrix} = \begin{bmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \end{bmatrix} \begin{pmatrix} x_1 \\\\ x_2 \end{pmatrix}$$ #### 6. Piecewise Functions & Cases ```latex $$f(n) = \begin{cases} \frac{n}{2} & \text{if } n \equiv 0 \pmod{2} \\ 3n + 1 & \text{if } n \equiv 1 \pmod{2} \end{cases}$$ ``` $$f(n) = \begin{cases} \frac{n}{2} & \text{if } n \equiv 0 \pmod{2} \\\\ 3n + 1 & \text{if } n \equiv 1 \pmod{2} \end{cases}$$ --- ### KaTeX vs. XeLaTeX: What Is and Is Not Supported | Feature | KaTeX (Browser Math Engine) | Full XeLaTeX / pdfLaTeX | | :--- | :--- | :--- | | **Execution Environment** | Client-side JavaScript DOM rendering | Server-side CLI TeX compiler (`xelatex`) | | **Mathematical Formulas (`\frac`, `\int`, `\sum`)** | **YES** (Full TeX math subset) | **YES** | | **Inline Math (`$x$`) & Block Math (`$$x$$`)** | **YES** | **YES** | | **Greek, Hebrew & Math Symbols** | **YES** (`\alpha, \beta, \Omega, \aleph`) | **YES** | | **Unicode in Math (`\text{日本語}`)** | **YES** (Direct UTF-8 support) | **YES** | | **Document Preambles (`\documentclass`)** | **NO** (Not a document compiler) | **YES** | | **Arbitrary LaTeX Packages (`\usepackage`)** | **NO** | **YES** | | **XeTeX FontSpec & System TTF Embedding** | **NO** | **YES** | --- --- ## 2. Comprehensive Symbol & Character Reference Tables Below is the complete reference of scientific, mathematical, typographic, and special symbols available in BookStack using **TeX Math (KaTeX)** and **Standard HTML/Unicode**. ### 2.1 Units, Angles, Temperature & Physics Symbols | Symbol Name | TeX Math Code | TeX Rendered | HTML Entity / Code | HTML Rendered | Example Usage | | :--- | :--- | :---: | :--- | :---: | :--- | | **Degree (Angle / Temp)** | `^\circ` or `^\circ\text{C}` | $^\circ$, $25^\circ\text{C}$ | `°` or `°` | ° | `$\theta = 90^\circ$`, `72°F` | | **Degree Fahrenheit** | `^\circ\text{F}` | $77^\circ\text{F}$ | `°F` | °F | `$T = 68^\circ\text{F}$` | | **Ohm (Resistance)** | `\Omega` or `\text{k}\Omega` | $\Omega$, $\text{k}\Omega$ | `Ω` | Ω | `$R_1 = 4.7\text{k}\Omega$` | | **Micro (Prefix)** | `\mu` or `\mu\text{F}` | $\mu$, $\mu\text{F}$ | `µ` | µ | `$C = 100\mu\text{F}$`, `µs` | | **Delta (Change / Diff)** | `\Delta` or `\delta` | $\Delta$, $\delta$ | `Δ`, `δ` | Δ, δ | `$\Delta V = 1.2\text{ V}$` | | **H-bar (Planck Constant)** | `\hbar` | $\hbar$ | `ℏ` | ℏ | `$\hbar = \frac{h}{2\pi}$` | | **Angstrom (Wavelength)** | `\text{\AA}` or `\mathring{\text{A}}` | $\text{\AA}$ | `Å` | Å | `$\lambda = 5500\text{ \AA}$` | | **Angle** | `\angle`, `\measuredangle` | $\angle$, $\measuredangle$ | `∠` or `∠` | ∠ | `$\angle ABC = 45^\circ$` | | **Perpendicular / Orthogonal** | `\perp` | $\perp$ | `⊥` | ⊥ | `$\vec{A} \perp \vec{B}$` | | **Parallel** | `\parallel` | $\parallel$ | `∥` | ∥ | `$L_1 \parallel L_2$` | | **Infinity** | `\infty` | $\infty$ | `∞` | ∞ | `$\lim_{x \to \infty} f(x)$` | | **Proportional To** | `\propto` | $\propto$ | `∝` | ∝ | `$F \propto \frac{1}{r^2}$` | | **Approximately Equal** | `\approx`, `\sim` | $\approx$, $\sim$ | `≈` | ≈ | `$x \approx 3.14$` | | **Plus-Minus / Minus-Plus** | `\pm`, `\mp` | $\pm$, $\mp$ | `±` | ± | `$V_{\text{out}} = 5\text{V} \pm 5\%$` | | **Multiplication / Dot** | `\times`, `\cdot` | $\times$, $\cdot$ | `×`, `·` | ×, · | `$A \times B$, $A \cdot B$` | | **Division** | `\div` | $\div$ | `÷` | ÷ | `$a \div b$` | --- ### 2.2 Complete Greek Alphabet Reference | Letter Name | Lowercase TeX | Rendered | Uppercase TeX | Rendered | HTML Lower / Upper | | :--- | :--- | :---: | :--- | :---: | :--- | | **Alpha** | `\alpha` | $\alpha$ | `A` | $A$ | `α` (α) / `Α` (Α) | | **Beta** | `\beta` | $\beta$ | `B` | $B$ | `β` (β) / `Β` (Β) | | **Gamma** | `\gamma` | $\gamma$ | `\Gamma` | $\Gamma$ | `γ` (γ) / `Γ` (Γ) | | **Delta** | `\delta` | $\delta$ | `\Delta` | $\Delta$ | `δ` (δ) / `Δ` (Δ) | | **Epsilon** | `\epsilon`, `\varepsilon` | $\epsilon$, $\varepsilon$ | `E` | $E$ | `ε` (ε) / `Ε` (Ε) | | **Zeta** | `\zeta` | $\zeta$ | `Z` | $Z$ | `ζ` (ζ) / `Ζ` (Ζ) | | **Eta** | `\eta` | $\eta$ | `H` | $H$ | `η` (η) / `Η` (Η) | | **Theta** | `\theta`, `\vartheta` | $\theta$, $\vartheta$ | `\Theta` | $\Theta$ | `θ` (θ) / `Θ` (Θ) | | **Iota** | `\iota` | $\iota$ | `I` | $I$ | `ι` (ι) / `Ι` (Ι) | | **Kappa** | `\kappa` | $\kappa$ | `K` | $K$ | `κ` (κ) / `Κ` (Κ) | | **Lambda** | `\lambda` | $\lambda$ | `\Lambda` | $\Lambda$ | `λ` (λ) / `Λ` (Λ) | | **Mu** | `\mu` | $\mu$ | `M` | $M$ | `μ` (μ) / `Μ` (Μ) | | **Nu** | `\nu` | $\nu$ | `N` | $N$ | `ν` (ν) / `Ν` (Ν) | | **Xi** | `\xi` | $\xi$ | `\Xi` | $\Xi$ | `ξ` (ξ) / `Ξ` (Ξ) | | **Pi** | `\pi`, `\varpi` | $\pi$, $\varpi$ | `\Pi` | $\Pi$ | `π` (π) / `Π` (Π) | | **Rho** | `\rho`, `\varrho` | $\rho$, $\varrho$ | `P` | $P$ | `ρ` (ρ) / `Ρ` (Ρ) | | **Sigma** | `\sigma`, `\varsigma` | $\sigma$, $\varsigma$ | `\Sigma` | $\Sigma$ | `σ` (σ) / `Σ` (Σ) | | **Tau** | `\tau` | $\tau$ | `T` | $T$ | `τ` (τ) / `Τ` (Τ) | | **Upsilon** | `\upsilon` | $\upsilon$ | `\Upsilon` | $\Upsilon$ | `υ` (υ) / `Υ` (Υ) | | **Phi** | `\phi`, `\varphi` | $\phi$, $\varphi$ | `\Phi` | $\Phi$ | `φ` (φ) / `Φ` (Φ) | | **Chi** | `\chi` | $\chi$ | `X` | $X$ | `χ` (χ) / `Χ` (Χ) | | **Psi** | `\psi` | $\psi$ | `\Psi` | $\Psi$ | `ψ` (ψ) / `Ψ` (Ψ) | | **Omega** | `\omega` | $\omega$ | `\Omega` | $\Omega$ | `ω` (ω) / `Ω` (Ω) | --- ### 2.3 Calculus, Operators & Matrix Formats | Operation / Concept | TeX Math Code | Rendered Output | | :--- | :--- | :---: | | **Definite / Indefinite Integral** | `\int_{a}^{b} f(x) \text{ } dx` | $\int_{a}^{b} f(x) \text{ } dx$ | | **Contour / Surface Integral** | `\oint_C \vec{B} \cdot d\vec{\ell}`, `\iint_S \vec{E} \cdot d\vec{A}` | $\oint_C \vec{B} \cdot d\vec{\ell}$, $\iint_S \vec{E} \cdot d\vec{A}$ | | **Summation & Product** | `\sum_{k=1}^{n} k^2`, `\prod_{i=1}^{n} x_i` | $\sum_{k=1}^{n} k^2$, $\prod_{i=1}^{n} x_i$ | | **Partial Derivatives & Nabla** | `\frac{\partial^2 \psi}{\partial x^2}`, `\nabla \times \vec{B}` | $\frac{\partial^2 \psi}{\partial x^2}$, $\nabla \times \vec{B}$ | | **Limits** | `\lim_{x \to 0} \frac{\sin x}{x} = 1` | $\lim_{x \to 0} \frac{\sin x}{x} = 1$ | | **Square & Nth Roots** | `\sqrt{x^2 + y^2}`, `\sqrt[3]{V}` | $\sqrt{x^2 + y^2}$, $\sqrt[3]{V}$ | | **Vectors & Hats** | `\vec{v}`, `\mathbf{E}`, `\hat{n}`, `\dot{x}`, `\ddot{\theta}` | $\vec{v}$, $\mathbf{E}$, $\hat{n}$, $\dot{x}$, $\ddot{\theta}$ | | **Matrix (Parentheses)** | `\begin{pmatrix} a & b \\ c & d \end{pmatrix}` | $\begin{pmatrix} a & b \\\\ c & d \end{pmatrix}$ | | **Matrix (Brackets)** | `\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}` | $\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \end{bmatrix}$ | | **Determinant / Magnitude** | `\begin{vmatrix} x & y \\ z & w \end{vmatrix}` | $\begin{vmatrix} x & y \\\\ z & w \end{vmatrix}$ | --- ### 2.4 Logic, Set Theory & Relational Symbols | Category | TeX Math Code | Rendered | HTML Entity / Code | | :--- | :--- | :---: | :--- | | **Quantifiers** | `\forall x`, `\exists y`, `\nexists z` | $\forall x$, $\exists y$, $\nexists z$ | `∀` (∀), `∃` (∃) | | **Set Membership** | `x \in A`, `y \notin B`, `\emptyset` | $x \in A$, $y \notin B$, $\emptyset$ | `∈` (∈), `∉` (∉), `∅` (∅) | | **Subsets & Supersets** | `A \subset B`, `A \subseteq B`, `A \cup B`, `A \cap B` | $A \subset B$, $A \subseteq B$, $A \cup B$, $A \cap B$ | `⊂` (⊂), `⊆` (⊆), `∪` (∪), `∩` (∩) | | **Logic Relations** | `P \land Q`, `P \lor Q`, `\neg P` | $P \land Q$, $P \lor Q$, $\neg P$ | `∧` (∧), `∨` (∨), `¬` (¬) | | **Implication & Equivalence** | `P \implies Q`, `P \iff Q`, `A \equiv B` | $P \implies Q$, $P \iff Q$, $A \equiv B$ | `⇒` (⇒), `⇔` (⇔), `≡` (≡) | | **Conclusions** | `\therefore`, `\because`, `\blacksquare`, `\Box` | $\therefore$, $\because$, $\blacksquare$, $\Box$ | `∴` (∴), `∵` (∵) | --- ### 2.5 Arrows & Signal Flow Symbols | Arrow Direction / Type | TeX Math Code | Rendered | HTML Entity | | :--- | :--- | :---: | :--- | | **Right / Left Arrow** | `\rightarrow`, `\leftarrow`, `\leftrightarrow` | $\rightarrow$, $\leftarrow$, $\leftrightarrow$ | `→` (→), `←` (←), `↔` (↔) | | **Long Right / Left** | `\longrightarrow`, `\longleftarrow`, `\longleftrightarrow` | $\longrightarrow$, $\longleftarrow$, $\longleftrightarrow$ | `⟶` (⟶), `⟵` (⟵) | | **Up / Down Arrow** | `\uparrow`, `\downarrow`, `\updownarrow` | $\uparrow$, $\downarrow$, $\updownarrow$ | `↑` (↑), `↓` (↓) | | **Double Implies Arrows** | `\Rightarrow`, `\Leftarrow`, `\Leftrightarrow` | $\Rightarrow$, $\Leftarrow$, $\Leftrightarrow$ | `⇒` (⇒), `⇐` (⇐), `⇔` (⇔) | | **Mapping / Yields** | `\mapsto`, `\longmapsto`, `\rightharpoonup` | $\mapsto$, $\longmapsto$, $\rightharpoonup$ | `↦` (↦) | --- ### 2.6 Typographic & Standard Wiki HTML Entities | Character / Symbol | HTML Entity | Decimal Code | Rendered | Common Use Case | | :--- | :--- | :--- | :---: | :--- | | **Degree Symbol** | `°` | `°` | **°** | Angles (`45°`), Temperatures (`72°F`, `22°C`) | | **Em Dash** | `—` | `—` | **—** | Long punctuation breaks — like this | | **En Dash** | `–` | `–` | **–** | Number ranges (e.g. pp. 10–15, 2020–2026) | | **Non-Breaking Space** | ` ` | ` ` | ` ` | Prevents unwanted line-breaks between values and units | | **Left / Right Smart Double Quotes** | `“`, `”` | `“`, `”` | **“ ”** | Publication-quality quotation marks | | **Left / Right Smart Single Quotes** | `‘`, `’` | `‘`, `’` | **‘ ’** | Apostrophes and single quotations | | **Fractions (Vulgar)** | `½`, `¼`, `¾` | `½`, `¼`, `¾` | **½, ¼, ¾** | Inline fractions without invoking full TeX | | **Copyright / Registered / Trademark** | `©`, `®`, `™` | `©`, `®`, `™` | **©, ®, ™** | Legal and branding designations | | **Checkmark / Crossmark** | `✓`, `✗` | `✓`, `✗` | **✓, ✗** | Verification and status indicators | | **Bullet / Middle Dot** | `•`, `·` | `•`, `·` | **•, ·** | Lists and inline separators | --- ## 3. Japanese Typography & Furigana (Ruby Text) BookStack fully supports **HTML5 Ruby Annotations** (`` and ``) for rendering Japanese Furigana (reading glosses placed above Kanji characters). ### Furigana Syntax & Examples #### Whole-Word Furigana ```html 漢字かんじ 東京とうきょう ``` * **Rendered Output:** 漢字かんじ, 東京とうきょう #### Per-Character Furigana (Fine-Grained Alignment) ```html 振ふり仮が名な 電でん波ぱ ``` * **Rendered Output:** 振ふり仮が名な, 電でん波ぱ #### Japanese Text Inside TeX Math Blocks Japanese characters can be rendered directly inside math equations using `\text{...}`: ```latex $$\text{周波数 } f = 433.92\text{ MHz} \qquad \text{周期 } T_e = 291.27\text{ }\mu\text{s}$$ ``` $$\text{周波数 } f = 433.92\text{ MHz} \qquad \text{周期 } T_e = 291.27\text{ }\mu\text{s}$$ --- ## 4. General Markdown & HTML Features Supported ### 3.1 Native BookStack Callout Alert Boxes BookStack provides colored callout boxes for contextual notes: ```html

Info Note: Background context and informational details.

Success: Empirical zero-drift test passed with 0 samples drift.

Warning: Ensure Word Clock is 75Ω terminated on the final device.

Danger / Critical: Never run recursive find commands on host ul.

``` **Rendered Output:**

Info Note: Background context and informational details.

Success: Empirical zero-drift test passed with 0 samples drift.

Warning: Ensure Word Clock is 75Ω terminated on the final device.

Danger / Critical: Never run recursive find commands on host ul.

--- ### 3.2 Collapsible Details & Accordions ```html
Click to expand technical registers

Detailed hardware memory offsets and bitfields go here.

``` **Rendered Output:**
Click to expand technical registers

Detailed hardware memory offsets and bitfields go here.

--- ### 3.3 Scaled Lightbox Images with Captions ```html

BookStack Interface Figure 1: Example styled gallery image with lightbox link

``` **Rendered Output:**

BookStack Interface Figure 1: Example styled gallery image with lightbox link

--- ### 3.4 YouTube Video Embedding BookStack supports direct HTML5 ` ``` **Rendered Output:** --- #### Method B: Raw YouTube Share Embed Snippet (Default Copy-Paste) This is the default, unstyled iframe code copied directly from YouTube's **Share $\rightarrow$ Embed** modal (`560` × `315`). It uses fixed pixel dimensions without `max-width: 100%`, which maintains a strict fixed size on desktop, but may require horizontal scrolling on narrow mobile viewports: ```html ``` **Rendered Output:** --- #### Method C: Lightweight Thumbnail Link (Markdown Fallback) When an active video iframe is not required or when optimizing for strict privacy environments, use a high-resolution YouTube video thumbnail with an external link: ```markdown [![Watch Video](https://img.youtube.com/vi/dQw4w9WgXcQ/hqdefault.jpg)](https://www.youtube.com/watch?v=dQw4w9WgXcQ) ``` **Rendered Output:** [![Watch Video](https://img.youtube.com/vi/dQw4w9WgXcQ/hqdefault.jpg)](https://www.youtube.com/watch?v=dQw4w9WgXcQ) --- ## 5. Summary Guide for Authors & AI Agents 1. **Math Formulas**: Use standard `$$ ... $$` for display equations and `$ ... $` for inline math. 2. **Avoiding Underscore Collisions**: Multiple unescaped underscores in a formula (e.g. `VAR_1 ... VAR_2`) can trigger Markdown italics (``). Use hyphens (e.g. `\text{DRATE-M}`) or single subscripts (`x_1`) to prevent Markdown parser mangling. 3. **Japanese / Furigana**: Use `漢字かんじ` in Markdown, or `\text{...}` in KaTeX equations. 4. **Callout Boxes**: Use `

` for styled alert banners. 5. **Code Safety**: Shell commands (`$ sudo ...`) inside `

` or `` code blocks are automatically preserved and never evaluated as math.
6. **YouTube Embeds**: Use `