Crate sophy 

Sophy 🧮

Sophy is a lightweight, efficient, and extensible mathematical library written in pure Rust. It provides numerical methods, mathematical functions, and number utilities for scientific computing, educational tools, and general-purpose applications.

✨ Features

• 🔢 Numerical Methods: Newton-Raphson root finding, integration, interpolation
• 📊 Mathematical Functions: Exponential, logarithmic, trigonometric functions
• 🧮 Number Utilities: Base operations, number theory functions
• 🦀 Pure Rust: Memory-safe, zero-cost abstractions
• 📚 Well Documented: Comprehensive documentation with examples
• 🧪 Well Tested: Extensive test suite with high coverage

🚀 Quick Start

Add Sophy to your Cargo.toml:

[dependencies]
sophy = "0.1.23"

📖 Examples

Newton-Raphson Root Finding

Find the square root of 2 using Newton-Raphson method:

use sophy::methods::raphson::raphson;

// Define the function f(x) = x² - 2
let f = |x: f64| x * x - 2.0;
// Define its derivative f'(x) = 2x
let df = |x: f64| 2.0 * x;

// Find the root starting from x₀ = 1.0
let root = raphson(1.0, f, df, 1e-10, 100);

println!("√2 ≈ {:.10}", root); // Output: √2 ≈ 1.4142135624
assert!((root - std::f64::consts::SQRT_2).abs() < 1e-10);

Base Number Operations

Work with mathematical constants and utilities:

use sophy::base::numbers::{PI, EULER, PHI};

println!("π = {:.6}", PI);       // π = 3.141593
println!("e = {:.6}", EULER);    // e = 2.718282
println!("φ = {:.6}", PHI);      // φ = 1.618034

Special Mathematical Functions

Advanced mathematical functions for scientific computing:

use sophy::specials::{gamma, zeta, erf};

// Gamma function: Γ(5) = 4! = 24
let factorial_4 = gamma(5.0);

// Riemann zeta function: ζ(2) = π²/6
let zeta_2 = zeta(2.0);

// Error function for probability calculations
let error_val = erf(1.0);

🏗️ Architecture

Sophy is organized into focused modules:

• methods: Numerical methods for solving mathematical problems
• base: Fundamental number operations and utilities
• specials: Special mathematical functions (gamma, zeta, erf, etc.)

🔬 Precision & Performance

Sophy uses f64 precision by default for optimal balance between accuracy and performance. All algorithms are implemented with numerical stability in mind.

🤝 Contributing

Contributions are welcome! Please see our contributing guide for details.

📜 License

This project is dual-licensed under the MIT License or Apache License 2.0.

Modules

base

Base Mathematical Operations Module

methods

Numerical Methods Module

specials

Special Mathematical Functions Module