latex_math_evaluator 0.1.4

A Dart library for parsing and evaluating mathematical expressions in LaTeX format.

LaTeX Math Evaluator 🧮

A Flutter/Dart library designed for parsing and evaluating complex mathematical expressions in native LaTeX format. Built for researchers, engineers, and educators who need symbolic accuracy and broad notation support.

Note

This library is under active development. Check our Roadmap 🚚 for upcoming features.

✨ Key Capabilities

• 🎯 Native LaTeX Parsing – Evaluate expressions directly from academic papers without manual translation.
• 🧮 Symbolic Calculus – Compute exact derivatives and simplify expressions using algebraic rules.
• 🔢 Advanced Mathematics – Support for summations, products, limits, integrals, and special functions.
• 🏗️ Linear Algebra – Full suite of matrix and vector operations, including determinants and powers.
• 🛡️ Type-Safe Results – Robust handling of Real, Complex, Matrix, and Vector types via Dart 3 sealed classes.
• 🚩 Domain Awareness – Uses an Assumptions System (e.g., $x > 0$) to ensure mathematically sound transformations.
• 🔧 Extensible Architecture – Easily add custom LaTeX commands and evaluation logic.
• 🧩 Implicit/Explicit Logic – Natural parsing of $2\pi r$ or $\sin 2x$—no need to type every *. easy to switch between implicit and explicit logic.

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🚀 Quick Start

Add the dependency to your pubspec.yaml:

dependencies:
  latex_math_evaluator: ^0.1.3

Basic Evaluation

import 'package:latex_math_evaluator/latex_math_evaluator.dart';

final evaluator = LatexMathEvaluator();

// 1. Simple numeric result
final result = evaluator.evaluateNumeric(r'\frac{\sqrt{16}}{2} + \sin{\pi}'); 
print(result); // 2.0

// 2. Evaluation with variables
final vars = {'x': 3.0, 'y': 4.0};
final hypotenuse = evaluator.evaluateNumeric(r'\sqrt{x^2 + y^2}', vars);
print(hypotenuse); // 5.0

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🛠️ Core Features

1. Symbolic Calculus & Differentiation 📐

Unlike libraries that use numeric approximations, latex_math_evaluator can compute exact symbolic derivatives.

final expr = evaluator.parse(r'x^3 + \sin{x}');

// Compute symbolic derivative: 3x^2 + cos(x)
final derivative = evaluator.differentiate(expr, 'x');

// Evaluate at x = 0
print(evaluator.evaluateParsed(derivative, {'x': 0})); // 1.0 (cos(0))

2. Complex & Multi-Dimensional Math 🏗️

Handle matrices, vectors, and complex numbers as first-class citizens.

// Matrix multiplication and power
final matrixResult = evaluator.evaluate(r'''
  \begin{pmatrix} 0.8 & 0.1 \\ 0.2 & 0.7 \end{pmatrix} ^ 2
''');

// Complex numbers (i or j notation)
final complexResult = evaluator.evaluate(r'(1 + 2i) \cdot (3 - 4i)');

3. High-Fidelity Diagnostics 🔍

Get precise feedback when parsing fails, including the exact position and helpful suggestions.

final validation = evaluator.validate(r'\frac{1{2}');
if (!validation.isValid) {
  print('Error at ${validation.position}: ${validation.errorMessage}');
  // Output: Error at 10: Expected '}' after numerator
}

4. Performance & Caching ⚡

For applications requiring frequent evaluations (like graphing or simulations), use the built-in LRU cache.

// Configure a 512-entry cache for parsed ASTs
final fastEvaluator = LatexMathEvaluator(parsedExpressionCacheSize: 512);

// Subsequent calls with the same string are near-instant
fastEvaluator.evaluate(r'\sum_{i=1}^{100} i'); 

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📚 Real-World Examples

Domain	LaTeX Expression	Capability
Physics	\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}	Lorentz Factor (Variable Binding)
Engineering	\frac{P L^3}{48 E I} ( 3 \frac{x}{L} - 4 ( \frac{x}{L} )^3 )	Beam Deflection (Algebraic)
Quantum	\int_{0}^{L} \psi^*(x) \hat{H} \psi(x) dx	Expectation Values (Integration)
Statistics	\frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}	Normal Distribution (Constants)

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📖 Documentation & Resources

• Getting Started
• Symbolic Algebra – Simplification and expansion rules.
• Function Reference – List of all supported LaTeX commands.
• Extending the Library – How to add custom functions.
• Performance Guide – Tuning the cache and memoization.

🤝 Contributing

We welcome contributions of all kinds! Whether it's reporting a bug, improving documentation, or adding a new mathematical feature.

1. Fork the repository.
2. Create your feature branch.
3. Commit your changes.
4. Push to the branch and open a Pull Request.

📄 License

This project is licensed under the MIT License. See the LICENSE file for details.

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Built with ❤️ for the scientific community.