numthy 0.1.0b0

Computational number theory. Pure Python. Zero dependencies. Unreasonably fast.

Computational number theory. Pure Python. Zero dependencies. Unreasonably fast.

Installation

pip install numthy

Or save numthy.py directly into your project.

Quick Start

import numthy as nt

# Primality testing
nt.is_prime(2**89 - 1)  # True (Mersenne prime)

# Factorization
nt.prime_factors(2**64 + 1)  # (274177, 67280421310721)

# Modular arithmetic
nt.discrete_log(3, 1000, 2**16 + 1)  # 50921

# Diophantine equations
solutions = nt.pell(2)
next(solutions)  # (3, 2) since 3² - 2·2² = 1

Highlights

The same algorithms used by Mathematica, SageMath, and research-grade CAS systems — implemented from scratch in pure Python.

• Primality — Miller-Rabin, Baillie-PSW, Lucas-Lehmer
• Factorization — Brent's variant of Pollard's rho, Lenstra's ECM (Elliptic Curve Method), Self-Initializing Quadratic Sieve with up to 3 large primes
• Prime counting — Lagarias-Miller-Odlyzko combinatorial method
• Discrete log — Pohlig-Hellman, Baby-step giant-step, Pollard rho
• Modular roots — Tonelli-Shanks, Adleman-Manders-Miller for arbitary k-th roots, Hensel lifting with both simple and multiple roots
• Diophantine — Cornacchia, Pell solver, binary quadratic forms, Pillai's equation
• Lattices — LLL reduction, Babai's nearest plane, Smith normal form

Documentation

See API.md for the full API reference.

Requirements

Python 3.10+

That's it.

License

Free to use, copy, modify, and redistribute with attribution.