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skills/docx/references/math-formulas.md
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skills/docx/references/math-formulas.md
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# Math Formulas — LaTeX → docx-js Mapping
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## Design Philosophy
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GLM uses **LaTeX as the formula input syntax**, internally converting to docx-js Math objects.
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**Why not write OMML directly?**
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- Models are naturally proficient in LaTeX (abundant in training data)
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- LaTeX is semantically clear and highly readable
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- Conversion layer is encapsulated internally, transparent to the user
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## Quick Start
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```js
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const { Math: OoxmlMath, MathRun, MathFraction, MathSuperScript,
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MathSubScript, MathRadical, MathSum, MathSubSuperScript } = require("docx");
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// Embed formula in paragraph
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new Paragraph({
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alignment: AlignmentType.CENTER,
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children: [
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new OoxmlMath({
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children: [/* Math components */]
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})
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]
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})
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```
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## LaTeX → docx-js Conversion Table
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### Basic Operations
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| LaTeX | Meaning | docx-js Implementation |
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|-------|---------|----------------------|
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| `x + y` | Addition | `new MathRun("x + y")` |
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| `x - y` | Subtraction | `new MathRun("x − y")` (use Unicode minus `−`) |
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| `x \times y` | Multiplication | `new MathRun("x × y")` |
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| `x \div y` | Division | `new MathRun("x ÷ y")` |
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| `x \pm y` | Plus-minus | `new MathRun("x ± y")` |
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| `x \neq y` | Not equal | `new MathRun("x ≠ y")` |
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| `x \leq y` | Less or equal | `new MathRun("x ≤ y")` |
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| `x \geq y` | Greater or equal | `new MathRun("x ≥ y")` |
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### Fractions
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| LaTeX | docx-js |
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|-------|---------|
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| `\frac{a}{b}` | `new MathFraction({ numerator: [new MathRun("a")], denominator: [new MathRun("b")] })` |
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| `\frac{x+1}{x-1}` | `new MathFraction({ numerator: [new MathRun("x+1")], denominator: [new MathRun("x−1")] })` |
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### Superscripts & Subscripts
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| LaTeX | docx-js |
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|-------|---------|
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| `x^2` | `new MathSuperScript({ children: [new MathRun("x")], superScript: [new MathRun("2")] })` |
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| `x_i` | `new MathSubScript({ children: [new MathRun("x")], subScript: [new MathRun("i")] })` |
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| `x_i^2` | `new MathSubSuperScript({ children: [new MathRun("x")], subScript: [new MathRun("i")], superScript: [new MathRun("2")] })` |
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### Radicals
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| LaTeX | docx-js |
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|-------|---------|
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| `\sqrt{x}` | `new MathRadical({ children: [new MathRun("x")] })` |
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| `\sqrt[3]{x}` | `new MathRadical({ children: [new MathRun("x")], degree: [new MathRun("3")] })` |
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### Summation & Integrals
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| LaTeX | docx-js |
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|-------|---------|
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| `\sum_{i=1}^{n}` | `new MathSum({ subScript: [new MathRun("i=1")], superScript: [new MathRun("n")], children: [new MathRun("aᵢ")] })` |
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### Greek Letters
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Use Unicode characters directly:
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```js
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// LaTeX → Unicode mapping
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const GREEK = {
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"\\alpha": "α", "\\beta": "β", "\\gamma": "γ", "\\delta": "δ",
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"\\epsilon": "ε", "\\zeta": "ζ", "\\eta": "η", "\\theta": "θ",
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"\\iota": "ι", "\\kappa": "κ", "\\lambda": "λ", "\\mu": "μ",
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"\\nu": "ν", "\\xi": "ξ", "\\pi": "π", "\\rho": "ρ",
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"\\sigma": "σ", "\\tau": "τ", "\\phi": "φ", "\\chi": "χ",
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"\\psi": "ψ", "\\omega": "ω",
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"\\Alpha": "Α", "\\Beta": "Β", "\\Gamma": "Γ", "\\Delta": "Δ",
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"\\Theta": "Θ", "\\Lambda": "Λ", "\\Pi": "Π", "\\Sigma": "Σ",
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"\\Phi": "Φ", "\\Psi": "Ψ", "\\Omega": "Ω",
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};
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```
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## Complete Formula Examples
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### Quadratic Formula
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LaTeX: `x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}`
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```js
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new OoxmlMath({
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children: [
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new MathRun("x = "),
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new MathFraction({
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numerator: [
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new MathRun("−b ± "),
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new MathRadical({
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children: [
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new MathSuperScript({
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children: [new MathRun("b")],
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superScript: [new MathRun("2")],
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}),
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new MathRun(" − 4ac"),
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],
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}),
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],
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denominator: [new MathRun("2a")],
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}),
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],
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})
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```
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### Pythagorean Theorem
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LaTeX: `a^2 + b^2 = c^2`
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```js
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new OoxmlMath({
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children: [
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new MathSuperScript({ children: [new MathRun("a")], superScript: [new MathRun("2")] }),
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new MathRun(" + "),
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new MathSuperScript({ children: [new MathRun("b")], superScript: [new MathRun("2")] }),
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new MathRun(" = "),
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new MathSuperScript({ children: [new MathRun("c")], superScript: [new MathRun("2")] }),
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],
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})
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```
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### Trigonometric Identity
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LaTeX: `\sin^2\theta + \cos^2\theta = 1`
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```js
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new OoxmlMath({
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children: [
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new MathSuperScript({ children: [new MathRun("sin")], superScript: [new MathRun("2")] }),
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new MathRun("θ + "),
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new MathSuperScript({ children: [new MathRun("cos")], superScript: [new MathRun("2")] }),
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new MathRun("θ = 1"),
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],
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})
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```
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## Common Exam Formula Templates
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### Middle School Math
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```js
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// Quadratic discriminant
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const discriminant = new OoxmlMath({
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children: [
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new MathRun("Δ = "),
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new MathSuperScript({ children: [new MathRun("b")], superScript: [new MathRun("2")] }),
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new MathRun(" − 4ac"),
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],
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});
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// Circle area
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const circleArea = new OoxmlMath({
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children: [
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new MathRun("S = π"),
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new MathSuperScript({ children: [new MathRun("r")], superScript: [new MathRun("2")] }),
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],
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});
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```
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### High School Math
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```js
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// Logarithm change of base
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const logChange = new OoxmlMath({
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children: [
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new MathSubScript({ children: [new MathRun("log")], subScript: [new MathRun("a")] }),
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new MathRun("b = "),
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new MathFraction({
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numerator: [new MathRun("ln b")],
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denominator: [new MathRun("ln a")],
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}),
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],
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});
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// Arithmetic series sum
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const arithmeticSum = new OoxmlMath({
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children: [
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new MathSubScript({ children: [new MathRun("S")], subScript: [new MathRun("n")] }),
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new MathRun(" = "),
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new MathFraction({
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numerator: [
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new MathRun("n("),
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new MathSubScript({ children: [new MathRun("a")], subScript: [new MathRun("1")] }),
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new MathRun(" + "),
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new MathSubScript({ children: [new MathRun("a")], subScript: [new MathRun("n")] }),
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new MathRun(")"),
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],
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denominator: [new MathRun("2")],
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}),
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],
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});
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```
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### Physics
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```js
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// Newton's second law
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const newton2 = new OoxmlMath({
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children: [new MathRun("F = ma")],
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});
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// Kinetic energy
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const kineticEnergy = new OoxmlMath({
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children: [
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new MathSubScript({ children: [new MathRun("E")], subScript: [new MathRun("k")] }),
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new MathRun(" = "),
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new MathFraction({
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numerator: [new MathRun("1")],
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denominator: [new MathRun("2")],
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}),
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new MathRun("m"),
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new MathSuperScript({ children: [new MathRun("v")], superScript: [new MathRun("2")] }),
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],
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});
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```
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## Complexity Fallback Strategy
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When formulas are too complex (nesting >3 levels) for docx-js Math, **fall back to matplotlib PNG rendering:**
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```python
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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def latex_to_png(latex_str: str, output_path: str, fontsize: int = 14, dpi: int = 200):
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"""Render LaTeX formula as PNG image"""
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fig, ax = plt.subplots(figsize=(0.1, 0.1))
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ax.axis("off")
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text = ax.text(0, 0.5, f"${latex_str}$", fontsize=fontsize,
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transform=ax.transAxes, verticalalignment="center")
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fig.canvas.draw()
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bbox = text.get_window_extent(fig.canvas.get_renderer())
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fig.set_size_inches(bbox.width / dpi + 0.2, bbox.height / dpi + 0.2)
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plt.savefig(output_path, dpi=dpi, bbox_inches="tight",
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pad_inches=0.05, transparent=True)
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plt.close()
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return output_path
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```
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Then embed the PNG in the document:
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```js
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const formulaImg = fs.readFileSync("formula.png");
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new Paragraph({
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alignment: AlignmentType.CENTER,
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children: [new ImageRun({
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data: formulaImg,
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transformation: { width: 300, height: 40 }, // adjust based on actual size
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type: "png",
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})],
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})
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```
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**Fallback rules:**
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- Nested fractions >2 levels → fallback
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- Matrices/determinants → fallback
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- Complex integrals (multiple integrals + limits + integrand) → fallback
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- Piecewise functions → fallback
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- All other cases → prefer docx-js Math
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