SymbAnaFis: Symbolic Analysis for Physics

A fast, focused Rust library for symbolic differentiation and analysis, designed for physics and engineering applications.

Features

Symbolic Differentiation: Compute derivatives of complex mathematical expressions.
Context-Aware Parsing: Support for fixed variables (constants) and custom functions.
Simplification: Comprehensive algebraic, trigonometric, hyperbolic, and logarithmic simplification rules.
Extensible: Easily add new functions and simplification rules.
Safe: Built with Rust's safety guarantees, with limits on recursion depth and node count.

Installation

Add this to your Cargo.toml:

[dependencies]
symb_anafis = "0.1.0"

Quick Start

use symb_anafis::{diff, simplify};

fn main() {
    // Differentiate sin(x) * x with respect to x
    let derivative = diff(
        "sin(x) * x".to_string(),
        "x".to_string(),
        None, // No fixed variables
        None  // No custom functions
    ).unwrap();

    println!("Derivative: {}", derivative);
    // Output: cos(x) * x + sin(x)

    // Simplify an expression
    let simplified = simplify(
        "x^2 + 2*x + 1".to_string(),
        None, // No fixed variables
        None  // No custom functions
    ).unwrap();

    println!("Simplified: {}", simplified);
    // Output: (x + 1)^2
}

Configuration

You can configure safety limits using environment variables:

SYMB_ANAFIS_MAX_DEPTH: Maximum AST depth (default: 100)
SYMB_ANAFIS_MAX_NODES: Maximum AST node count (default: 10000)

export SYMB_ANAFIS_MAX_DEPTH=200
export SYMB_ANAFIS_MAX_NODES=50000

Advanced Usage

Expression Simplification

You can simplify expressions without differentiation:

use symb_anafis::simplify;

fn main() {
    // Simplify a complex expression
    let result = simplify(
        "sin(x)^2 + cos(x)^2".to_string(),
        None, // No fixed variables
        None  // No custom functions
    ).unwrap();

    println!("Simplified: {}", result);
    // Output: 1
}

Multi-Character Symbols

For symbols with multiple characters (like "sigma", "alpha", etc.), pass them as fixed variables to ensure they're treated as single symbols:

use symb_anafis::simplify;

fn main() {
    // This treats "sigma" as one symbol
    let result = simplify(
        "(sigma^2)^2".to_string(),
        Some(&["sigma".to_string()]),
        None
    ).unwrap();
    println!("Simplified: {}", result);
    // Output: sigma^4
}

Fixed Variables and Custom Functions

You can define constants (like a, b) and custom functions (like f(x)) that are treated correctly during differentiation.

use symb_anafis::diff;

fn main() {
    // Differentiate a * f(x) with respect to x
    let result = diff(
        "a * f(x)".to_string(),
        "x".to_string(),
        Some(&["a".to_string()]),       // 'a' is a constant
        Some(&["f".to_string()])        // 'f' is a custom function
    ).unwrap();

    println!("Derivative: {}", result);
    // Output: a * ∂_f(x)/∂_x
}

Supported Functions

Trigonometric: sin, cos, tan, cot, sec, csc, asin, acos, atan, acot, asec, acsc
Hyperbolic: sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh, acoth, asech, acsch
Exponential/Logarithmic: exp, ln, log, log10, log2
Roots: sqrt, cbrt
Absolute Value/Sign: abs, sign
Special: sinc, erf, erfc, gamma, digamma, trigamma, tetragamma, polygamma, beta, LambertW, besselj, bessely, besseli, besselk

Note: The polygamma(n, x) function provides derivatives for all polygamma functions. Functions with non-elementary derivatives use custom notation.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

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

symb_anafis 0.2.4