Introduction

TeXpr is a Dart library that parses and evaluates mathematical expressions using LaTeX syntax. It converts strings like \frac{\sqrt{16}}{2} + \sin{\pi} into numeric results.

Why TeXpr?

Consider these scenarios:

• Scientific calculator app: Users type expressions, you need to evaluate them
• Graphing tool: Generate y-values for thousands of x-values from a formula
• Education platform: Parse and validate student-submitted equations
• Engineering application: Evaluate formulas with different parameter values

TeXpr handles the parsing, evaluation, and edge cases so you can focus on your application.

What TeXpr Does

Capability	Example
Parse LaTeX	\sqrt{x^2 + y^2} → AST
Evaluate expressions	3 + 4 * 2 → 11.0
Handle variables	x^2 with x=3 → 9.0
Complex numbers	e^{i\pi} → -1 + 0i
Matrix operations	Matrix multiplication, determinants
Symbolic calculus	Differentiate, integrate, limits

What TeXpr Is NOT

To set expectations correctly:

• Not a CAS: TeXpr doesn't simplify 2x + 3x to 5x. It evaluates expressions to numeric/symbolic results, but doesn't perform algebraic simplification beyond basic rules.
• Not a full LaTeX parser: It handles math notation, not document formatting (\documentclass, \begin{theorem}, etc.)
• Not arbitrary precision: Uses IEEE 754 doubles (~15 digits of precision)

See Known Issues for detailed limitations.

How It Works (In Brief)

TeXpr processes expressions through a pipeline:

"\sin{x} + 1"  →  Tokenizer  →  Parser  →  Evaluator  →  1.84...
                     ↓            ↓           ↓
                  Tokens        AST       Result

1. Tokenizer: Breaks input into tokens (numbers, operators, functions)
2. Parser: Builds a tree structure (AST) from tokens
3. Evaluator: Computes the result by traversing the tree

For details, see How It Works.

Quick Example

import 'package:texpr/texpr.dart';

final evaluator = Texpr();

// Simple evaluation
final result = evaluator.evaluate(r'\sqrt{16} + \sin{\pi}');
print(result.asNumeric());  // 4.0

// With variables
final hypotenuse = evaluator.evaluate(
  r'\sqrt{x^2 + y^2}', 
  {'x': 3.0, 'y': 4.0}
);
print(hypotenuse.asNumeric());  // 5.0

// Symbolic differentiation
final derivative = evaluator.differentiate(r'x^3', 'x');
final slope = evaluator.evaluateParsed(derivative, {'x': 2.0});
print(slope.asNumeric());  // 12.0

Next Steps

• Installation – Add TeXpr to your project
• Quick Start – Get productive in 5 minutes
• Core Concepts – Understand key ideas
• Boolean Logic – Logic operators and comparisons
• Piecewise Functions – Conditional expressions and cases
• API Reference – Complete method documentation