LaTeX to Math.js Converter

A robust JavaScript utility that converts LaTeX mathematical expressions into Math.js compatible syntax. This converter handles a wide range of mathematical notation including fractions, roots, trigonometric functions, logarithms, and complex nested expressions.

📋 Table of Contents

• Features
• Installation
• Usage
• Supported LaTeX Commands
• How It Works
• Examples
• Contributing
• License
• Star the Repository

✨ Features

• Comprehensive LaTeX Support: Handles fractions, roots, exponents, trigonometric functions, logarithms, and more
• Nested Expression Handling: Properly processes deeply nested mathematical expressions
• Implicit Multiplication: Automatically adds multiplication operators where needed (e.g., 2x → 2*x)
• Smart Function Recognition: Distinguishes between mathematical functions and variable names
• Absolute Value Support: Converts both \left| \right| and simple | | notation
• Reciprocal Trig Functions: Handles \sec, \csc, \cot by converting to their reciprocal forms

📦 Installation

Simply import the function into your JavaScript project:

import { latexToMathJs } from './LatexToMathJs.js';

Or if using CommonJS:

const { latexToMathJs } = require('./LatexToMathJs.js');

🚀 Usage

import { latexToMathJs } from './LatexToMathJs.js';

// Basic usage
const latex = '\\frac{x^2 + 1}{2}';
const mathJs = latexToMathJs(latex);
console.log(mathJs); // Output: ((x^(2))+1)/(2))

// With Math.js evaluation
import { evaluate } from 'mathjs';

const result = evaluate(mathJs, { x: 3 });
console.log(result); // Output: 5

📚 Supported LaTeX Commands

Fractions

• \frac{numerator}{denominator} → ((numerator)/(denominator))

Roots

• \sqrt{x} → sqrt(x)
• \sqrt[n]{x} → (x^(1/n))

Trigonometric Functions

• Standard: \sin, \cos, \tan
• Inverse: \arcsin, \arccos, \arctan, \sin^{-1}, \cos^{-1}, \tan^{-1}
• Reciprocal: \sec, \csc, \cot (converted to 1/cos, 1/sin, 1/tan)

Logarithms

• \ln{x} → log(x) (natural logarithm)
• \log{x} → log10(x) (base 10)

Exponentials and Powers

• \exp{x} → exp(x)
• e^{x} → exp(x)
• x^{n} → (x^(n))
• x^2 → (x^2)

Absolute Value

• \left| x \right| → abs(x)
• |x| → abs(x)

Constants

• \pi → pi
• \e → e
• \infty → Infinity

Operators

• \cdot → *
• \times → *
• \div → /
• \pm → + (plus-minus treated as plus)

Brackets

• \left(, \right), \left[, \right], \left\{, \right\} → ()

🔧 How It Works

The converter processes LaTeX expressions through several carefully ordered stages:

1. Absolute Value Conversion (First Priority)

// Handles \left| ... \right| and | ... |
expr = expr.replace(/\\left\|([^|]+)\\right\|/g, 'abs($1)');

Absolute values are processed first to prevent interference with other operators.

2. Fraction Handling (Recursive)

// Recursively handles nested fractions
do {
    prevExpr = expr;
    expr = expr.replace(/\\frac\{([^{}]*(?:\{[^{}]*\}[^{}]*)*)\}\{([^{}]*(?:\{[^{}]*\}[^{}]*)*)\}/g,
        '(($1)/($2))');
} while (expr !== prevExpr);

Uses a loop to handle deeply nested fractions like \frac{\frac{a}{b}}{c}.

3. Root Conversion

// nth roots and square roots
expr = expr.replace(/\\sqrt\[([^\]]+)\]\{([^}]+)\}/g, '(($2)^(1/($1)))');
expr = expr.replace(/\\sqrt\{([^}]+)\}/g, '(sqrt($1))');

4. Trigonometric Functions (Order Matters!)

Inverse functions are processed before regular ones to prevent incorrect conversions:

// Inverse trig first
expr = expr.replace(/\\arctan/g, 'atan');
// Then regular trig
expr = expr.replace(/\\tan/g, 'tan');

5. Function Arguments

Handles functions with explicit arguments and space-separated notation:

// sin x → sin(x)
expr = expr.replace(/sin\s+([a-zA-Z])/g, 'sin($1)');

6. Power and Exponent Handling

// Special case: e^{...} → exp(...)
expr = expr.replace(/e\^\{([^}]+)\}/g, 'exp($1)');
// General powers: x^{n} → (x^(n))
expr = expr.replace(/([a-zA-Z0-9]+)\^\{([^}]+)\}/g, '($1^($2))');

7. Implicit Multiplication (Smart Detection)

This is the most complex part, using a state machine approach:

const knownFuncs = ['sin', 'cos', 'tan', 'asin', 'acos', 'atan', ...];

while (i < expr.length) {
    // Check if current position starts a known function
    if (matchedFunc) {
        // Don't add multiplication within function names
    } else if (isVariable) {
        // Add * between consecutive variables (xy → x*y)
        // But NOT between variable and function (xsin → x*sin, not xs*in)
    }
}

The algorithm handles:

• Number + variable: 2x → 2*x
• Variable + variable: xy → x*y (but preserves function names like sin)
• Number + parenthesis: 2(x) → 2*(x)
• Closing + opening parens: )( → )*(
• Variable + parenthesis: x(y) → x*(y) (except for functions)

8. Cleanup

Final step removes remaining LaTeX backslashes and extra spaces.

📖 Examples

Basic Expressions

latexToMathJs('x^2 + 2x + 1');
// Output: (x^2)+2*x+1

latexToMathJs('\\frac{1}{2}x');
// Output: ((1)/(2))*x

Trigonometric

latexToMathJs('\\sin(x) + \\cos(x)');
// Output: sin(x)+cos(x)

latexToMathJs('\\sec(x)');
// Output: (1/cos(x))

latexToMathJs('\\arctan(y)');
// Output: atan(y)

Complex Nested Expressions

latexToMathJs('\\frac{\\sin(x)}{\\cos(x)}');
// Output: ((sin(x))/(cos(x)))

latexToMathJs('\\sqrt{\\frac{a^2 + b^2}{c}}');
// Output: (sqrt(((a^(2))+(b^(2)))/(c)))

latexToMathJs('e^{-\\frac{x^2}{2}}');
// Output: exp(-((x^(2))/(2)))

Absolute Values

latexToMathJs('\\left| x - 1 \\right|');
// Output: abs(x-1)

latexToMathJs('|x| + |y|');
// Output: abs(x)+abs(y)

Implicit Multiplication

latexToMathJs('2xy');
// Output: 2*x*y

latexToMathJs('(x+1)(x-1)');
// Output: (x+1)*(x-1)

latexToMathJs('\\pi r^2');
// Output: pi*r^(2)

🤝 Contributing

We welcome contributions! If you find any bugs or have suggestions for improvements, please:

Reporting Bugs

1. Check existing issues to avoid duplicates
2. Create a new issue with:
   • Clear description of the bug
   • Input LaTeX expression
   • Expected output
   • Actual output
   • Steps to reproduce

Submitting Pull Requests

1. Fork the repository
2. Create a new branch (git checkout -b feature/your-feature-name)
3. Make your changes
4. Add tests if applicable
5. Commit your changes (git commit -m 'Add some feature')
6. Push to the branch (git push origin feature/your-feature-name)
7. Open a Pull Request

Development Guidelines

• Maintain the existing code style
• Add comments for complex logic
• Update the README if adding new features
• Test with various LaTeX expressions

Areas for Contribution

• Additional LaTeX command support
• Performance optimizations
• Better error handling
• More comprehensive test coverage
• Documentation improvements

⭐ Star the Repository

If you find this project useful, please consider giving it a star on GitHub! It helps others discover the project and motivates continued development.

⭐ Star this repository

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🔗 Related Projects

• Math.js - Extensive math library for JavaScript
• KaTeX - Fast math typesetting library
• MathJax - Beautiful math in all browsers

📞 Support

If you need help or have questions:

• Open an issue on GitHub
• Check existing documentation
• Review the examples above

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Made with ❤️ for the mathematical community