LMath – The Ultimate Mathematics Library for JavaScript/Node.js

LMath is a comprehensive, modular, and high-performance mathematics library for JavaScript and Node.js. It covers everything from basic arithmetic to advanced calculus, linear algebra, statistics, complex numbers, differential equations, and numerical methods. Designed with clarity, extensibility, and educational value in mind, LMath is perfect for students, researchers, and developers who need powerful mathematical tools.

✨ Features

• 100% Pure JavaScript – Works in Node.js and browsers (with bundlers).

• Modular Architecture – Import only what you need.

• High Precision – BigInt support for large integers, rational numbers, and complex arithmetic.

• Comprehensive Coverage – Over 500 functions across multiple domains:

  • ➕ Arithmetic – Basic operations, number theory, combinatorics, sequences.
  • 🧮 Algebra – Vectors, matrices, linear systems, decompositions (LU, QR, SVD, Cholesky), eigenvalues.
  • 📈 Calculus – Limits, derivatives, integrals (multiple methods), ODEs, PDEs, series.
  • 📊 Statistics – Descriptive statistics, probability distributions, hypothesis tests, regression.
  • 🌀 Complex Numbers – Full complex arithmetic, trig, hyperbolic, roots, exponentials.
  • 🔢 Number Theory – Primes, GCD/LCM, modular arithmetic, arithmetic functions.
  • 🔬 Numerical Methods – Root finding, optimization, numerical integration, FFT.
  • 🎲 Random Numbers – Multiple PRNGs (Xorshift, Mersenne Twister), distributions, sampling.

• Well Documented – Every function includes JSDoc comments with examples.

• Tested – Extensive test suite covering edge cases.

📦 Installation

npm install lmath

Or include directly in HTML (using a CDN):

<script src="https://cdn.jsdelivr.net/npm/lmath/dist/lmath.min.js"></script>

🚀 Quick Start

// Import the whole library
const lmath = require('lmath');

// Or import specific modules
const { add, mul, sqrt } = require('lmath/core/arithmetic');
const { solveLinear, eigen } = require('lmath/core/linearAlgebra');
const { normalPDF, correlation } = require('lmath/core/statistics');
const { Complex, rk4 } = require('lmath/advanced');

// Basic arithmetic
console.log(add(5, 3));                // 8
console.log(sqrt(16));                  // 4
console.log(factorial(5));              // 120

// Linear algebra
const A = [[1, 2], [3, 4]];
const b = [5, 6];
console.log(solveLinear(A, b));         // [-4, 4.5]
console.log(det(A));                     // -2

// Statistics
const data = [2, 4, 4, 4, 5, 5, 7, 9];
console.log(mean(data));                 // 5
console.log(stdDev(data));               // 2.138
console.log(correlation([1,2,3], [2,4,6])); // 1.0

// Complex numbers
const z1 = new Complex(3, 4);
const z2 = new Complex(1, -2);
console.log(z1.mul(z2).toString());     // "11 - 2i"

// Differential equations
const f = (x, y) => y;                   // dy/dx = y
const sol = rk4(f, 0, 1, 2, 100);
console.log(sol[sol.length-1].y);        // ≈ 7.389 (e^2)

📚 Module Overview

LMath is organized into three main directories:

📁 core/ – Essential, everyday math

Module Description Key Functions arithmetic.js Basic operations, number theory, combinatorics add, gcd, factorial, isPrime, fibonacci, binomial algebra.js Vectors, matrices, linear algebra dotProduct, matrixMul, det, inv, eigen calculus.js Derivatives, integrals, ODEs, series derivative, integral, rk4, taylorSeries linearAlgebra.js Extended linear algebra lu, qr, svd, cholesky, conjugateGradient complex.js Complex numbers Complex class with all operations statistics.js Statistics and probability mean, variance, normalPDF, correlation, tTest

📁 advanced/ – Specialized topics

| Module | Description Key | Functions |

differentialEquations.js, ODE solvers, BVP, PDEs rk4, rkf45, shootingMethod, heatEquation

📁 utils/ – Utilities and helpers

Module Description Key Functions random.js Random number generation normal, poisson, shuffle, uuidv4 constants.js Mathematical, physical, astronomical constants PI, E, G, C, SOLAR_MASS, GOLDEN_RATIO

🧪 Testing

Run the test suite:

npm test

Tests cover all modules with edge cases and performance benchmarks.

🤝 Contributing

Contributions are welcome! Please follow the contribution guidelines.

1. Fork the repository.
2. Create a feature branch.
3. Write tests for new functionality.
4. Submit a pull request.

##📄 License

LMath is MIT licensed. © 2026 Eduardo Amorim Pereira.

🙏 Acknowledgments

· Inspired by NumPy, SciPy, Math.js, and Python's math module. · Thanks to the open-source community for providing foundational algorithms and ideas.

🚀 What's Next?

We're constantly expanding LMath. Planned future modules include:

· Machine Learning – Basic algorithms (linear regression, k-means, neural networks) · Graph Theory – Dijkstra, Floyd–Warshall, spanning trees · Quantum Computing – Simulated quantum gates and algorithms · Fractals – Mandelbrot, Julia sets, L-systems

Stay tuned!