numnerd 0.0.3

A Python library for nerdy mathematical functions and number theory.

numnerd 🤓

numnerd is a Python library dedicated to the pursuit of numerical excellence and the exploration of integer properties. The library currently features exactly 73 specialized functions, providing a comprehensive toolkit for the modern number theorist.

Whether you are seeking the next Mersenne prime, navigating the recursive paths of the Collatz conjecture, or calculating $\pi$ to a precision that would make a circle blush, numnerd provides the necessary tools.

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🛠 Installation

You can install numnerd via pip:

pip install numnerd

Note: For those with a collaboration distance of zero to the source, cloning the repository is also an option.

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🚀 Quick Start

Integration is straightforward. No complex axioms required.

from numnerd import is_prime, fibonacci, calculate_pi, is_happy_number

# Primality check
is_prime(17) # True

# The 10th term of the Fibonacci sequence
fibonacci(10) # 55

# Detecting "Happy" integers
is_happy_number(19) # True

# High-precision constants
calculate_pi(50)

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📚 The Collection

Organized into four fundamental modules, the library provides a comprehensive toolkit for mathematical discovery.

🔢 Building Blocks (primes)

Tools for the analysis of primality and divisibility.

• Classification: is_prime, is_perfect_number, is_sophie_germain_prime, is_twin_prime, is_mersenne_prime, is_chen_prime, is_fermat_prime.
• Arithmetic Functions: prime_factorization, euler_totient ($\phi$), mobius_function ($\mu$), prime_pi ($\pi(n)$).
• Search & Selection: sieve_of_eratosthenes, lcm, next_prime, prev_prime.
• Conjectures: goldbach_partition.

🌀 Recursive Logic (sequences)

Exotic and classical integer sequences.

• Foundations: fibonacci, lucas_number, catalan_number, triangular_number, pell_number, collatz_path.
• Growth & Patterns: look_and_say, lazy_caterer, thue_morse_iteration, recaman_sequence, padovan_sequence, sylvester_sequence.
• Combinatorial: bell_number, motzkin_number, juggler_sequence, golomb_sequence, perrin_number, narayana_cows.
• Chaotic Systems: hofstadter_q, van_eck_sequence, wythoff_sequences.

🃏 Numerical Oddities (recreational)

Properties that emerge from the digits themselves.

• Self-Referential: is_armstrong_number, is_munchausen_number, is_disarium_number, is_neon_number, is_kaprekar_number, is_automorphic_number.
• Digit Dynamics: kaprekar_routine (6174), digital_root, is_spy_number, is_keith_number, is_vampire_number, is_polydivisible_number.
• Divisor Relations: is_abundant_number, is_deficient_number, is_smith_number, is_pronic_number, is_happy_number.

♾️ Fundamental Constants (constants)

Arbitrary-precision calculation of the universe's most important ratios.

• Universal Ratios: calculate_pi, calculate_e, calculate_golden_ratio, calculate_silver_ratio.
• Roots & Logarithms: calculate_sqrt2, calculate_ln2, calculate_gauss_constant.
• Physical & Mathematical Limits: calculate_catalan_constant, calculate_universal_parabolic_constant, calculate_aperys_constant, calculate_gelfond_constant, calculate_omega_constant, calculate_levy_constant.

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🧪 Verification

We value rigor. The library maintains a 1:1 ratio of functions to tests.

python run_tests.py

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📜 License

This project is licensed under the MIT License. As Paul Erdős would say, "A mathematician is a device for turning coffee into theorems"—this library is simply the byproduct of that process.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." – Bertrand Russell