Crate numbers_rus 

numbers_rus

A number-theory and exact-arithmetic toolkit for Rust, organised around three pillars:

1. Number theory — deterministic Miller-Rabin primality, Sieve of Eratosthenes, wheel-factored integer factorization, GCD/LCM via the binary Euclidean algorithm, modular exponentiation and inversion, Euler’s totient, and the Chinese Remainder Theorem. See integers::primes and integers::arith.
2. Exact arithmetic — generic rational::Rational over any signed integer type (auto-reducing), and generic complex::Complex with full operator overloading.
3. Symbolic objects — typed equation::Equation and single-variable equation::Polynomial with Horner evaluation, differentiation, and arithmetic.

A lightweight stats module rounds this out with mean, median, variance, std_dev, quartiles, and iqr over any slice of a numeric type convertible to f64.

Quick tour

use numbers_rus::integers::{primes, arith, sequences};
use numbers_rus::rational::Rational;
use numbers_rus::equation::{Equation, Op, Polynomial};

// Primality in microseconds, even for large u64.
assert!(primes::is_prime(1_000_003));
assert!(!primes::is_prime(1_000_004));

// Modular arithmetic for crypto-adjacent problems.
assert_eq!(arith::mod_pow(2, 10, 1000), 24);
assert_eq!(arith::mod_inverse(3, 11), Some(4));

// Exact rationals.
let r = Rational::new(2i64, 4) + Rational::new(1, 3);
assert_eq!(format!("{}", r), "5/6");

// Typed equations (no sentinel-value bugs).
let mut eq = Equation::new(0i64, 0, Op::Add);
assert_eq!(eq.solve(), 0); // zero is a valid solution, not "not computed"

// Polynomials.
let p = Polynomial::new(vec![1, 0, -1]); // 1 - x^2
assert_eq!(p.eval(3), -8);

Feature flags

• std (default) — enables std-dependent APIs (currently everything; no_std support is planned for a future release).
• serde — derives Serialize and Deserialize on rational::Rational, complex::Complex, equation::Equation, equation::Op, and equation::Polynomial.

Migrating from 0.2

The 1.0 release is a substantial reshape. See the CHANGELOG for the full rename table; the highlights:

• solve::equation::Equation::get_sol() is now equation::Equation::solve, backed by Option<T> rather than a 0 sentinel.
• integers::base::is_prime is replaced by integers::primes::is_prime (Miller-Rabin, deterministic for u64).
• single::single_vector::* is replaced by stats, which takes &[T] and returns numeric results instead of String.
• structures::dataframe, vector::vector, and numbers::complex have been removed.

Modules

complex

Generic complex numbers a + bi.

equation

Symbolic equation objects.

integers

Integer algorithms, grouped by family.

rational

Exact rational arithmetic generic over any signed integer type.

stats

Descriptive statistics for numeric slices.