Adding `mathcore_nostd` library as a dependency

Run this command in a terminal, in your project's directory:

cargo add mathcore_nostd

To add it manually, edit your project's Cargo.toml file and add to the [dependencies] section:

mathcore_nostd = "0.3.2"

The mathcore_nostd library will be automatically available globally. Read the mathcore_nostd library documentation.

Back to the crate overview.

Readme

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. This is a fork of the original mathcore library to work in no_std environments. This is not guaranteed to work in any environment and will probably not be actively maintained.

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_nostd in your project's root directory.

Option 2: Add to your Cargo.toml:

[dependencies]
mathcore_nostd = "0.3.1"

Quick example

use mathcore_nostd::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

use mathcore_nostd::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

use mathcore_nostd::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

use mathcore_nostd::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

use mathcore_nostd::ml::{Optimization, SymbolicIntegration};
use alloc::collections::BTreeMap

// 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 = BTreeMap::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

let math = MathCore::new();
let mut vars = BTreeMap::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

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

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

Complex Numbers

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

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

Integration

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

Equation Solving

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!

# run tests
cargo test

# benchmarks
cargo bench

# docs
cargo doc --open

License

MIT

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Adding mathcore_nostd library as a dependency

Adding `mathcore_nostd` library as a dependency