# MathCore
[](https://crates.io/crates/mathcore)
[](https://docs.rs/mathcore)
[](https://github.com/Nonanti/mathcore/actions)
[](https://opensource.org/licenses/MIT)
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
Add to your `Cargo.toml`:
```toml
[dependencies]
mathcore = "0.1.0"
```
## Quick example
```rust
use mathcore::MathCore;
use std::collections::HashMap;
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
```rust
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
```rust
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
```rust
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
```rust
use mathcore::ml::{Optimization, SymbolicIntegration};
// 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
```rust
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
```rust
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
```rust
let plot = MathCore::plot_ascii("sin(x)", "x", -3.14, 3.14, 60, 20).unwrap();
println!("{}", plot);
```
### Complex Numbers
```rust
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
```
### Differentiation
```rust
MathCore::differentiate("sin(x) * x^2", "x")
// Returns: (cos(x) * x^2 + sin(x) * 2*x)
```
### Integration
```rust
MathCore::integrate("2*x", "x")
// Returns: x^2
```
### Equation Solving
```rust
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!
```bash
# run tests
cargo test
# benchmarks
cargo bench
# docs
cargo doc --open
```
## License
MIT
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