TeXpr is a Dart library that parses and evaluates mathematical expressions using LaTeX syntax. It compiles input strings into an Abstract Syntax Tree (AST) to support numerical evaluation, symbolic differentiation, and structural analysis.
- 🎯 LaTeX Parsing – Parses standard LaTeX mathematical notation directly into Dart objects.
- 🧮 Symbolic Calculus – Computes derivatives and gradients (
\nabla) using algebraic rules. - 🔢 Advanced Mathematics – Supports summations, products, limits, integrals, and special functions.
- 📈 Linear Algebra – Supports matrix and vector operations, including determinants, inverses, and arithmetic.
- 🔢 Type Safety – Returns results as
Numeric,Complex,Matrix, orVectorvia Dart 3 sealed classes. - 🚩 Domain Constraints – Validates mathematical domains (e.g.,
$x > 0$ ) during evaluation. - 🧩 Implicit Multiplication – Supports implicit syntax such as
$2 \pi r^2$ or$\sin{2x}$ . (can be disabled) - 🎲 Equation Solving – Solves linear and quadratic equations symbolically.
- 🚦 Boolean Logic – Boolean algebra (
\land,\lor,\neg) and comparisons (>,\ge,=). - 🚨 Piecewise Functions – Evaluates and differentiates conditional expressions.
- ✨ Unicode Input – Accepts mathematical symbols directly:
√,∑,∫,π, Greek letters, and more.
Add the dependency to your pubspec.yaml:
dependencies:
texpr: ^0.1.4
import 'package:texpr/texpr.dart';
final evaluator = Texpr();
// 1. Numeric evaluation
final result = evaluator.evaluateNumeric(r'\frac{\sqrt{16}}{2} + \sin{\pi}');
print(result); // 2.0
// 2. Evaluation with variable binding
final vars = {'x': 3.0, 'y': 4.0};
final hypotenuse = evaluator.evaluateNumeric(r'\sqrt{x^2 + y^2}', vars);
print(hypotenuse); // 5.0
The library supports exact symbolic differentiation and gradient computation rather than finite difference approximations.
// Differentiate with respect to x
final derivative = evaluator.differentiate(r'x^3 + \sin{x}', 'x');
// Evaluate the derivative at x = 0
print(evaluator.evaluateParsed(derivative, {'x': 0})); // 1.0
// Compute Gradient (\nabla)
// Auto-discovers variables in the expression
final grad = evaluator.evaluate(r'\nabla{x^2 + y^2}', {'x': 1, 'y': 2});
print(grad.asVector()); // [2.0, 4.0]
// Differentiate piecewise functions
final piecewise = evaluator.differentiate(r'|\sin{x}|, -3 < x < 3', 'x');
print(evaluator.evaluateParsed(piecewise, {'x': 1})); // cos(1)Evaluates expressions involving complex numbers and linear algebra components.
// Euler's identity evaluation
final euler = evaluator.evaluate(r'e^{i*\pi}');
print(euler.asComplex().real); // -1.0
// Complex trigonometry
final sinComplex = evaluator.evaluate(r'\sin(1 + 2*i)');
print(sinComplex.asComplex()); // Complex(3.1658, 1.9596)
// Matrix arithmetic
final matrixResult = evaluator.evaluate(r'''
\begin{pmatrix} 0.8 & 0.1 \\ 0.2 & 0.7 \end{pmatrix} ^ 2
''');
- TexprException: Base class for all library exceptions.
- ValidationResult: Detailed validation information.
- Security Considerations: Overview of security mitigations and limits. The parser provides error location offsets and suggestions for syntax errors.
try {
evaluator.parse(r'\frac{1{2}');
} on TexprException catch (e) {
print('Error at ${e.position}: ${e.message}');
print('Suggestion: ${e.suggestion}');
}
// Function name suggestions
try {
evaluator.evaluate(r'\sinn{x}');
} on EvaluatorException catch (e) {
print(e.suggestion); // "Did you mean 'sin'?"
}
The Texpr includes a configurable multi-layer LRU cache for repeated evaluations.
// Parse once, evaluate multiple times (Recommended for loops)
final ast = evaluator.parse(r'\sin(x) + \cos(x)');
for (var x = 0.0; x < 100; x += 0.01) {
evaluator.evaluateParsed(ast, {'x': x});
}
| Mode | Overhead | Description |
|---|---|---|
evaluate() |
High | Parses and evaluates the string on every call. |
evaluateParsed() |
Low | Evaluates a pre-parsed AST. Recommended for loops. |
Important
Comparison Limitations: This performance reference compares different tools with different purposes:
- Dart: Numeric evaluation of LaTeX syntax
- Python: Symbolic computation with SymPy (capable of algebra, not just evaluation)
- JavaScript: General-purpose math with mathjs (supports units, matrices, complex types)
Direct speed comparisons should be interpreted with these architectural differences in mind.
Results from MacBook Air M1 8GB, macOS 15.7.2:
| Expression Category | Dart (µs) | Dart WASM (µs) | Python (SymPy)* (µs) | JS (mathjs) (µs) |
|---|---|---|---|---|
| Basic: Trigonometry | 1.10 | 3.38 | 34.23 | 5.28 |
| Basic: Power & Sqrt | 1.05 | 2.80 | 32.93 | 6.09 |
| Polynomial | 1.19 | 3.10 | 6.45 | 5.59 |
| Academic: Normal PDF | 4.76 | 10.77 | 211.05 | 19.46 |
| Calculus: Definite Integral | 1,415.93 | N/A | 1,811.45 | N/A |
Parsed expressions (AST) can be exported to other formats.
final expr = evaluator.parse(r'\int x^2 dx');
// Export to JSON for tooling/debugging
print(expr.toJson());
// Export to SymPy for Python interoperability
print(expr.toSymPy()); // Output: integrate(x**2, x)
Below is a selection of examples showcasing the library's capabilities.
| Category | Expression | Feature Used |
|---|---|---|
| Physics | \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} |
Variable Binding |
| Engineering | \frac{P L^3}{48 E I} ( 3 \frac{x}{L} - 4 ( \frac{x}{L} )^3 ) |
Algebraic Simplification |
| Quantum | \int_{0}^{L} \psi^*(x) \hat{H} \psi(x) dx |
Integration |
| Statistics | \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} |
Constants () |
- Guide Index
- Quick Start
- Installation
- API Reference
- LaTeX Grammar
- Functions
- Known Issues
- Performance
- Deprecation Migration (
validate/isValid)
Contributions are welcome. Please open a Pull Request or Issue on GitHub.
This project is licensed under the MIT License. See the LICENSE file for details.