README

Provides classes for Complex numbers, Rational numbers, Vectors, and Matrices.

License | Changelog | Documentation

Description

This package provides classes for working with complex numbers, rational numbers, vectors, and matrices in PHP.

Key Features:

• Complex numbers - Full support for complex arithmetic, trigonometry, transcendental functions, and polar/rectangular conversions
• Rational numbers - Exact fraction arithmetic using integer ratios, automatic simplification, and overflow detection
• Vectors - Element-wise arithmetic, dot and cross products, and array-style access
• Matrices - Matrix arithmetic, inverse, determinant, transpose, power, and matrix-vector multiplication
• Type flexibility - Methods accept int, float, string, or the respective class type
• Comprehensive testing - 100% code coverage with extensive test suites

Development and Quality Assurance / AI Disclosure

Claude Chat and Claude Code were used in the development of this package. The core classes were designed, coded, and commented primarily by the author, with Claude providing substantial assistance with code review, suggesting improvements, debugging, and generating tests and documentation. All code was thoroughly reviewed by the author, and validated using industry-standard tools including PHP_Codesniffer, PHPStan (to level 9), and PHPUnit to ensure full compliance with PSR-12 coding standards and comprehensive unit testing with 100% code coverage. This collaborative approach resulted in a high-quality, thoroughly-tested, and well-documented package delivered in significantly less time than traditional development methods.

Requirements

• PHP ^8.4
• galaxon/core

Installation

composer require galaxon/math

Classes

Complex

Immutable class for complex numbers (a + bi) with support for:

• Basic arithmetic operations (add, subtract, multiply, divide)
• Transcendental functions (exp, ln, log, pow, roots)
• Trigonometric and hyperbolic functions (sin, cos, tan, asin, acos, atan)
• Polar and rectangular form conversions
• Epsilon-based equality comparison
• String parsing and formatting

Rational

Immutable class for rational numbers (p/q) with support for:

• Exact arithmetic using integer ratios (no floating-point errors)
• Automatic reduction to simplest form (e.g., 6/8 → 3/4)
• Conversion to/from floats using continued fractions
• Overflow-safe integer operations
• Comparison operations with mixed types
• String parsing and formatting

Vector

Mutable numeric vector with support for:

• Element-wise arithmetic (add, subtract, scalar multiply, scalar divide)
• Dot product and cross product operations
• Exact and approximate equality comparison
• Conversion to arrays and matrices
• Array-style element access via the ArrayAccess interface
• String representation using box-drawing characters

Matrix

Mutable two-dimensional matrix with support for:

• Matrix arithmetic (add, subtract, multiply, divide)
• Matrix-vector multiplication using column vector convention
• Transpose, determinant, and inverse operations
• Matrix power with binary exponentiation (including negative powers)
• Row-level ArrayAccess interface (get/set rows as Vectors)
• String representation using box-drawing characters

Testing

The library includes comprehensive test coverage:

# Run all tests
vendor/bin/phpunit

# Run tests for specific class
vendor/bin/phpunit tests/Complex
vendor/bin/phpunit tests/Rational
vendor/bin/phpunit tests/Vector
vendor/bin/phpunit tests/Matrix

# Run with coverage (generates HTML report and clover.xml)
composer test

License

MIT License - see LICENSE for details

Support

• Issues: https://github.com/mossy2100/Galaxon-PHP-Math/issues
• Documentation: See docs/ directory for detailed class documentation
• Examples: See test files for comprehensive usage examples

For questions or suggestions, please open an issue.

Changelog

See CHANGELOG.md for version history and changes.