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Elementary Number Theory for Integers in Rust

Currently the fastest library for factorization and primality checking in the interval 0;2^64 that is available in Crates.io and possibly in the entire Rust-lang ecosystem. Algebraic definitions of primality and factorization are used, permitting checks like -127.is_prime() to return true and unique factorizations to be considered unsigned.

Currently implements these functions

Primality
Factorization
GCD
Euler totient
Integer radical (not sqrt)
K-free
Modular exponentiation and quadratic residues
Legendre symbol
Jacobi symbol
Smoothness

Additionally this library has an implementation of the previous NT functions for arbitrary-precision integers, plus some elementary arithmetic. Multiplication utilizes Karatsuba algorithm, otherwise all other arithmetic can be assumed to be naive.

Addition/subtraction
Multiplication
Euclidean Division
Extended Euclidean (EEA)
Conversion to and from radix-10 string
Successor function (+1)
SIRP-factorials
Conditional Interval Product (CIP factorial)
Sqrt/nth root
Exponentiation
Logarithms

Usage is fairly simple

// include NT functions
use number_theory::NumberTheory;
// include arbitrary-precision arithmetic
use number_theory::Mpz;
  // Sign, generally unnecessary for ENT
//use number_theory:Sign; 
let mersenne = Mpz::from_string("-127").unwrap(); 
assert_eq!(mersenne.is_prime(), true);
 // Or for a more complex example
 
 // check if x mod 1 === 0, trivial closure
 let modulo = |x: &u64| {if x%1==0{return true} return false};
 
  //Generate  872 factorial, using the above trivial function
 let mut factorial = Mpz::cip(1, 872,modulo);
 
 // Successor function, increment by one
 factorial.successor();
 
 // 872! + 1 is in-fact a factorial prime
 assert_eq!(factorial.is_prime(),true)

number-theory 0.0.6

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