math-latex-parser

A powerful (La)TeX mathematical expression parser. Unlike simple string-based parsers, it generates a full Abstract Syntax Tree (AST) while respecting mathematical operator precedence and associativity.

Install

``bash
npm i @scicave/math-latex-parser
`

Usage

$3

`js
const { parse } = require('@scicave/math-latex-parser');

// Basic arithmetic
const ast = parse('1 + 2 * 3^2');

// Complex LaTeX
const tex = String.raw\int_{0}^{\pi} \sin(x) dx + \frac{1}{2};
const ast2 = parse(tex);
`

For an expression like 12+3^6x \frac 1 {5+3}, the parser generates a structured tree:

!AST

$3

`html


`

---

Features

- Arithmetic Operations: Full support for addition, subtraction, multiplication, division, powers, and factorials.
- Unary Prefix Operators: Correct handling of +, -, \pm, \mp, \neg, and \lnot.
- LaTeX Commands: Supports \frac, \sqrt, \sum, \prod, \int, \operatorname, and more.
- Automatic Multiplication: Intelligently handles implicit multiplication like 2x or (a+b)(c+d).
- Extended Math Structures: Support for:
- Matrices: \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}
- Sets: \{ 1, 2, 3 \}
- Tuples: (1, 2, 3)
- Intervals: [a, b), (0, \infty)
- Absolute Value: |x| or \left| x \right|
- Ellipsis: Support for ..., \dots, \cdots, etc. inside sets, matrices, and series.

---

Operator Precedence

| Operator | Type | Precedence | Associativity |
| :----------------------------------------- | :--------- | :--------- | :------------ |
| ^ | Infix | 7 | Left-to-Right |
| ! | Postfix | 6 | N/A |
| Implicit Mult | Automult | 5 | Left-to-Right |
| +, -, \pm, \mp, \neg, \lnot | Prefix | 4 | N/A |
| *, /, \cdot | Infix | 3 | Left-to-Right |
| +, - | Infix | 2 | Left-to-Right |
| =, \neq, \approx, \le, \in, etc. | Infix | 1 | Left-to-Right |

---

Parser Options

The parse(tex, options) function accepts an optional configuration object.

`js
parse("...", {
autoMult: true, // Allow implicit multiplication like 2x
keepParentheses: false, // If true, wraps parenthesized expressions in a "parentheses" node
functions: ["f", "g"], // Custom function names to prioritize
builtinFunctions: ["..."], // Override or extend (using "...") default TeX functions
builtinLetters: ["..."], // Override or extend (using "...") default TeX Greek letters
extra: {
memberExpressions: true, // Allow e.g., p.x
sets: true,
matrices: true,
tuples: true,
intervals: true,
ellipsis: true // Can be object for granular control (sets, matrices, etc.)
}
});
`

---

API: The Node Class

Every parsed node is an instance of the Node class.

$3


- node.type: The type of the node (e.g., "number", "id", "operator", "function").
- node.args: An array of child nodes (if any).
- node.name: For identifiers, functions, and operators.
- node.value: For numbers.

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#### node.check(props, checkArgs = false)
Checks if the node matches the provided properties.
`js
node.check({ type: "operator", name: "+" });
`

#### node.contains(props, checkArgs = false)
Recursively checks if the node or any of its descendants match the properties. This is the recommended way to search the tree.
`js
// Check if an expression contains any variable named "x"
ast.contains({ type: "id", name: "x" });

// Check if there is any addition anywhere in the tree
ast.contains({ type: "operator", name: "+" });
`

#### node.checkType(type)
Syntactic sugar for node.type === type, but with safety. It will throw an error if the type string provided is not one of the valid Node types.
`js
node.checkType("operator"); // true or false
node.checkType("invalid_type"); // Throws Error
`

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The available types are accessible via Node.types:
- Node.types.NUMBER ("number")
- Node.types.ID ("id")
- Node.types.OPERATOR ("operator")
- Node.types.FUNCTION ("function")
- Node.types.FRAC ("frac")
- ... and more.

---

Contribute

We love open-source! Feel free to suggest AST improvements or performance enhancements.

`bash
npm install
npm run build:watch # Watch and build
npm run test:watch # Run tests on changes
``

License

MIT