Algebraic Numbers Library

Use when you need exact arithmetic, speed is not critical, and rational numbers aren't good enough.

Example:

```rust use algebraics::prelude::*; use algebraics::RealAlgebraicNumber as Number;

let two = Number::from(2);

// 2 is a rational number assert!(two.is_rational());

// 1/2 is the reciprocal of 2 let one_half = two.recip();

// 1/2 is also a rational number assert!(onehalf.isrational());

// 2^(1/4) let root = (&two).pow((1, 4));

// we can use all the standard comparison operators assert!(root != Number::from(3)); assert!(root < Number::from(2)); assert!(root > Number::from(1));

// we can use all of add, subtract, multiply, divide, and remainder let sum = &root + &root; let difference = &root - Number::from(47); let product = &root * &onehalf; let quotient = &onehalf / &root; let remainder = &root % &one_half;

// root is not a rational number assert!(!root.is_rational());

// the calculations are always exact assert_eq!((&root).pow(4), two);

// lets compute 30 decimal places of root let scale = Number::from(10).pow(30); let scaled = &root * scale; let digits = scaled.intointegertrunc(); asserteq!( digits.tostring(), 1189207115002721066717499970560u128.to_string() );

// get the minimal polynomial let othernumber = root + two.pow((1, 2)); asserteq!( &othernumber.minimalpolynomial().to_string(), "2 + -8X + -4X^2 + 0X^3 + 1X^4" );

// works with really big numbers let reallybig = Number::from(10000000000i64).pow(20) + Number::from(23); asserteq!( &reallybig.tointegerfloor().tostring(), "100000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000\ 000000000000000000023" ) ```

Python support

Using algebraics from Python:

bash python3 -m pip install algebraics==0.1.2

python from algebraics import RealAlgebraicNumber sqrt_2 = 2 ** (RealAlgebraicNumber(1) / 2) assert sqrt_2 * sqrt_2 == 2

Using algebraics in your own Rust project:

toml [dependencies.algebraics] version = "0.1.2" features = ["python"]

Developing algebraics:

bash cargo install maturin maturin develop --cargo-extra-args="--features python-extension"