8 releases
0.1.7 | Oct 10, 2024 |
---|---|
0.1.6 | Jul 15, 2024 |
0.1.1 | Mar 2, 2024 |
#458 in Math
170KB
4K
SLoC
finitelib
finitelib
is a library over advanced maths for finite groups, fields,
their extensions, multi precision operations and related things.
At the moment the library supports:
- Finite groups
- Finite fields (prime -
GF(p)
, splitting -GF(p^m)
, binary -GF(2^m)
, Montgomery representation) - Euclidean rings (including modular operations)
- Polynomials
- Multi precision operations over unsigned integers
- Converting
- Formatting
- Basic operations: addition, subtraction, product, division, bitwise operations
- Prime numbers: Fermat test, Miller-Rabin test, Legendre symbol, Tonelli–Shanks algorithm
Usage
Installation command:
cargo add finitelib
Or add this to your Cargo.toml
:
[dependencies]
finitelib = "0.1.7"
Basic example
use finitelib::prelude::*;
use finitelib::gf::prime::Prime as GF;
// Define 256-bit unsigned integer type
type U256 = bigi_of_bits!(256);
// Define an Euclidean ring over U256, that contains the correct basic
// math operations like addition, multiplication, Euclidean extended
// algorithm and so on.
let R256 = bigi_ring_for_bigi!(U256);
// Define a 256-bit prime number
let p = U256::from_decimal("67096435317933606252190858377894931905843553631817376158639971807689379094463");
// Define a finite field `GF(p)` with the prime characteristic `p`
let gf = GF::new(R256, p);
// Define two arbitrary numbers
let a = U256::from(3);
let b = U256::from(2);
// Perform division a / b inside the field
let c = gf.div(&a, &b).unwrap();
// Print the result as a decimal string
println!("{:?}", c.to_decimal());
// Perform multiplication
let d = gf.mul(&c, &b);
// Since multiplication is opposite to division `d` must be equal to `a`
assert_eq!(d, a);
Dependencies
~315KB