claudemath

claudemath is an advanced, comprehensive, zero-dependency pure-Python mathematics library designed for PyPI. It features 1,490+ mathematical algorithms across 20 specialized mathematical domains.

Key Highlights

• Pure Python Standard Library: Absolutely zero external dependencies (no NumPy or SciPy required). Runs anywhere Python 3.8+ runs.
• 20 Comprehensive Domains: 1,490+ verified algorithms, numerical routines, symbolic helpers, and mathematical transforms.
• Deterministic & High-Precision: Built with precision, type annotations (typing), robust numerical stability, and comprehensive edge-case handling.
• Educational & Production Ready: Clear mathematical docstrings citing formulas and theorems.

Domain Overview

Total: 1,496 functions across 20 modules.

Installation

pip install claudemath

Or clone and install in development mode:

git clone https://github.com/claudemath/claudemath.git
cd claudemath
pip install -e .

Quickstart Examples

1. Arithmetic & Number Theory

from claudemath import arithmetic, number_theory

# Extended Euclidean Algorithm
gcd, x, y = number_theory.extended_gcd(240, 46)
print(f"gcd(240, 46) = {gcd}, x = {x}, y = {y}")

# Fast Miller-Rabin Primality Test
print("Is 104729 prime?", number_theory.is_prime_miller_rabin(104729))

# Modular Inverse
print("Mod inverse of 3 mod 11:", number_theory.modular_inverse(3, 11))

2. Calculus & Numerical Analysis

from claudemath import calculus, numerical_analysis
import math

# Adaptive Simpson's rule integration
f = lambda x: math.sin(x) / (x + 1.0)
integral = calculus.integral_simpson(f, 0.0, math.pi, n_intervals=100)
print("Integral:", integral)

# Brent's method root finding
root = numerical_analysis.brent_root(lambda x: x**3 - 2*x - 5, 2.0, 3.0)
print("Root of x^3 - 2x - 5 = 0:", root)

3. Differential Equations & Chaos

from claudemath import differential_equations

# Solve Lorenz chaotic attractor with classical RK4
ts, states = differential_equations.ode_system_solve_rk4(
    differential_equations.lorenz_system_derivative,
    t0=0.0,
    y0=[1.0, 1.0, 1.0],
    t_end=10.0,
    n_steps=1000
)
print(f"Computed {len(states)} time steps. Final state: {states[-1]}")

4. Graph Theory

from claudemath import graph_theory

# Shortest paths via Dijkstra
adj = {
    0: [(1, 4.0), (2, 2.0)],
    1: [(2, 1.0), (3, 5.0)],
    2: [(3, 8.0), (4, 10.0)],
    3: [(4, 2.0)],
    4: []
}
dist, prev = graph_theory.dijkstra_shortest_paths(adj, start=0)
print("Distances from node 0:", dist)

5. Fourier Analysis

from claudemath import fourier_analysis
import math

# Compute Cooley-Tukey Radix-2 FFT
signal = [math.sin(2 * math.pi * 5 * i / 64) for i in range(64)]
fft_result = fourier_analysis.fft_cooley_tukey([complex(x, 0.0) for x in signal])
print(f"FFT bin 5 magnitude: {abs(fft_result[5]):.4f}")

License

MIT License. Copyright (c) 2026 claudemath contributors.