MathCore

A symbolic math library for Rust. Think of it as a computer algebra system (CAS) that can do symbolic differentiation, integration, equation solving, and more.

What it does

Basic stuff

• Parse math expressions from strings (with proper precedence)
• Work with symbols, not just numbers
• Differentiate and integrate symbolically
• Solve equations (linear, quadratic, and some higher degree)
• Complex number support
• ASCII plots (for quick visualization)
• Expression simplification
• Variables and substitution

Fancier features

• Limits (including one-sided and at infinity)
• Matrix operations and linear algebra
• Arbitrary precision arithmetic (BigInt/BigRational)
• Optimization (gradients, Hessian, autodiff)
• Taylor series expansion
• Numerical methods (Newton's method, gradient descent)
• ODEs and PDEs solvers
• FFT and signal processing

Installation

Option 1: Run cargo add mathcore in your project's root directory.

Option 2: Add to your Cargo.toml:

tomlCopy
[dependencies]
mathcore = "0.3.1"

Quick example

rustCopy
use mathcore::MathCore;

fn main() {
    let math = MathCore::new();
    
    // basic arithmetic
    let result = math.calculate("2 + 3 * 4").unwrap();
    println!("2 + 3 * 4 = {}", result);  // 14
    
    // take derivatives
    let derivative = MathCore::differentiate("x^2 + 2*x + 1", "x").unwrap();
    println!("d/dx(x^2 + 2*x + 1) = {}", derivative);  // 2*x + 2
    
    // solve equations
    let roots = MathCore::solve("x^2 - 4", "x").unwrap();
    println!("roots: {:?}", roots);  // [2, -2]
}

Advanced Usage

Limits

rustCopy
use mathcore::calculus::limits::{Limits, LimitDirection};

let expr = MathCore::parse("sin(x)/x").unwrap();
let limit = Limits::limit(&expr, "x", 0.0, LimitDirection::Both).unwrap();
println!("lim(x→0) sin(x)/x = {}", limit); // Should be 1

// Check continuity
let continuous = Limits::is_continuous_at(&expr, "x", 1.0).unwrap();
println!("Function is continuous: {}", continuous);

Matrix Operations

rustCopy
use mathcore::matrix::{SymbolicMatrix, LinearAlgebra};
use nalgebra::{DMatrix, DVector};

// Symbolic matrices
let matrix = SymbolicMatrix::from_vec(vec![
    vec![1.0, 2.0],
    vec![3.0, 4.0],
]).unwrap();

let det = matrix.determinant().unwrap();
println!("Determinant: {}", det);

// Solve linear system Ax = b
let a = DMatrix::from_row_slice(2, 2, &[1.0, 2.0, 3.0, 4.0]);
let b = DVector::from_row_slice(&[5.0, 11.0]);
let solution = LinearAlgebra::solve_system(&a, &b).unwrap();
println!("Solution: {:?}", solution);

Arbitrary Precision

rustCopy
use mathcore::precision::{PrecisionNumber, ArbitraryPrecision};

// Exact rational arithmetic
let a = PrecisionNumber::from_str_with_precision("1/3").unwrap();
let b = PrecisionNumber::from_str_with_precision("1/6").unwrap();
let sum = a.add(&b);
println!("1/3 + 1/6 = {}", sum); // Outputs: 1/2

// Compute π with arbitrary precision
let pi = ArbitraryPrecision::compute_pi(100);
println!("π ≈ {}", pi);

Optimization and Calculus

rustCopy
use mathcore::ml::{Optimization, SymbolicIntegration};
use std::collections::HashMap;

// Compute gradient
let loss = MathCore::parse("x^2 + y^2").unwrap();
let vars = vec!["x".to_string(), "y".to_string()];
let gradient = Optimization::gradient(&loss, &vars).unwrap();
println!("∇f = [{}, {}]", gradient[0], gradient[1]);

// Taylor series expansion
let func = MathCore::parse("exp(x)").unwrap();
let taylor = Optimization::taylor_series(&func, "x", 0.0, 5).unwrap();
println!("Taylor series: {}", taylor);

// Gradient descent optimization
let mut params = HashMap::new();
params.insert("x".to_string(), 10.0);
params.insert("y".to_string(), 10.0);
let optimized = Optimization::gradient_descent(
    &loss, params, 0.1, 100
).unwrap();
println!("Optimized parameters: {:?}", optimized);

Working with Variables

rustCopy
let math = MathCore::new();
let mut vars = HashMap::new();
vars.insert("a".to_string(), 3.0);
vars.insert("b".to_string(), 4.0);

let result = math.evaluate_with_vars("sqrt(a^2 + b^2)", &vars).unwrap();
println!("Distance: {}", result);

Symbolic Integration

rustCopy
let integral = MathCore::integrate("x^2", "x").unwrap();
println!("∫x² dx = {}", integral);

// Numerical integration
let area = MathCore::numerical_integrate("x^2", "x", 0.0, 1.0).unwrap();
println!("∫₀¹ x² dx = {}", area);

Function Plotting

rustCopy
let plot = MathCore::plot_ascii("sin(x)", "x", -3.14, 3.14, 60, 20).unwrap();
println!("{}", plot);

Complex Numbers

rustCopy
let math = MathCore::new();
let result = math.evaluate("(3+4i) * (2-i)").unwrap();
println!("(3+4i) * (2-i) = {}", result);

Supported Functions

Arithmetic Operations

• Addition: +
• Subtraction: -
• Multiplication: *
• Division: /
• Power: ^
• Modulo: %
• Factorial: !
• Absolute value: |x|

Trigonometric Functions

• sin(x), cos(x), tan(x)
• sec(x) (through derivatives)

Exponential & Logarithmic

• exp(x) - e^x
• ln(x) - Natural logarithm
• log(x, base) - Logarithm with custom base
• sqrt(x) - Square root

Utility Functions

• min(a, b, ...) - Minimum value
• max(a, b, ...) - Maximum value
• abs(x) - Absolute value

Mathematical Constants

The following constants are predefined:

• pi - π (3.14159...)
• e - Euler's number (2.71828...)
• tau - τ = 2π (6.28318...)

Expression Syntax

Basic Examples

2 + 3 * 4           # Arithmetic
x^2 - 5*x + 6       # Polynomial
sin(x) + cos(x)     # Trigonometric
e^x                 # Exponential (using constant e)
3! + 4!            # Factorials
|x - 5|            # Absolute value
3 + 4i             # Complex numbers

Differentiation

rustCopy
MathCore::differentiate("sin(x) * x^2", "x")
// Returns: (cos(x) * x^2 + sin(x) * 2*x)

Integration

rustCopy
MathCore::integrate("2*x", "x")
// Returns: x^2

Equation Solving

rustCopy
MathCore::solve("x^2 + x - 6", "x")
// Returns: [2, -3]

Performance

Pretty fast. Uses LTO in release builds. Some rough numbers:

• Expression parsing: ~1μs
• Differentiation: ~10μs for polynomials
• Matrix ops use nalgebra (which uses BLAS when available)
• Exact arithmetic with rationals (no precision loss)

When to use this

• Scientific computing (physics simulations, engineering calcs)
• ML/optimization (automatic differentiation)
• Education (demonstrating calculus concepts)
• Financial calculations (need exact arithmetic)
• Any time you need symbolic math in Rust

Contributing

PRs welcome!

bashCopy
# run tests
cargo test

# benchmarks
cargo bench

# docs
cargo doc --open

License

MIT

© 2025 Nonanti

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