Metadata-Version: 2.4
Name: hyqerionmath
Version: 0.5.0
Summary: A Python library with mathematical utilities: primality testing, factorization, sequence generation, boolean logic, and coordinate geometry.
Author-email: Hyqerion <hyqerion199@gmail.com>
License: MIT License
        
        Copyright (c) 2025 Hyqerion199
        
        Permission is hereby granted, free of charge, to any person obtaining a copy
        of this software and associated documentation files (the "Software"), to deal
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Keywords: math,prime,fibonacci,truth table,geometry,base conversion,amicable,armstrong
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Intended Audience :: Developers
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Development Status :: 3 - Alpha
Requires-Python: >=3.7
Description-Content-Type: text/markdown
License-File: LICENSE
Dynamic: license-file

# HyqerionMath

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[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT) <!-- Link assumes MIT License -->

A Python library providing supplementary mathematical utility functions, focusing on number theory, sequences, geometry, and competitive programming algorithms.

## Overview

HyqerionMath aims to offer helpful, well-tested math functions that extend Python's built-in `math` module. It is designed to be simple, efficient, and easy to use—making it a perfect companion for math competitions, algorithmic challenges, and general programming.

## Features

HyqerionMath includes:

### Primality Functions (`primality.py`)

- **`isprime(number: int) -> bool`**: Efficiently checks if a given integer `number` is a prime number. Returns `True` if prime, `False` otherwise.
- **`get_nth_prime(n: int) -> int`**: Finds the _n_-th prime number (1-based index). e.g., `get_nth_prime(5)` is 11.
- **`get_primes_in_index_range(start_index: int, end_index: int) -> List[int]`**: Returns a list containing primes from the `start_index`-th prime to the `end_index`-th prime (inclusive, 1-based).
- **`find_primes_between(lower_bound: int, upper_bound: int) -> List[int]`**: Returns a sorted list of all prime numbers `p` such that `lower_bound <= p <= upper_bound`.

### Factorization Functions (`factorization.py`)

- **`get_factors(number: int) -> List[int]`**: Finds all positive integer factors of a given `number`. e.g., `get_factors(12)` returns `[1, 2, 3, 4, 6, 12]`.
- **`get_proper_divisors(number: int) -> List[int]`**: Finds all positive factors of a number EXCEPT the number itself.
- **`sum_proper_divisors(number: int) -> int`**: Returns the sum of all proper divisors.
- **`are_amicable(a: int, b: int) -> bool`**: Checks if two numbers form an amicable pair.
- **`get_prime_factorization(number: int) -> List[int]`**: Returns a sorted list of the prime factors of `number` (including duplicates). e.g., `get_prime_factorization(20)` returns `[2, 2, 5]`.

### Sequence Functions (`sequences.py`)

- **`get_nth_fibonacci(n: int) -> int`**: Calculates the _n_-th Fibonacci number using 1-based indexing (F(1)=0, F(2)=1, F(3)=1...).
- **`fibonacci_mod(n: int, mod: int) -> int`**: Efficiently calculates the _n_-th Fibonacci number modulo `mod` without memory overflow.
- **`get_fibonacci_in_index_range(start_index: int, end_index: int) -> List[int]`**: Returns a list of Fibonacci numbers within a specific index range.
- **`get_nth_triangular(n: int) -> int`**: Returns the _n_-th triangular number `n(n+1)/2`.
- **`get_lazy_caterer(n: int) -> int`**: Returns the maximum number of pieces a circle can be cut into with _n_ straight cuts `(n^2 + n + 2)/2`.

### Digit & Base Functions (`digits.py`)

- **`get_digits(number: int, base: int = 10) -> list`**: Returns a list of the digits of a number in a specific base.
- **`is_armstrong(number: int) -> bool`**: Checks if a number is an Armstrong (Narcissistic) number.
- **`base_to_base10(string_val: str, base: int) -> int`**: Converts a string representation of a number in any base (2-36) to Base 10.
- **`get_champernowne_digit(n: int) -> int`**: Efficiently finds the _n_-th digit of the Champernowne constant sequence (123456789101112...) in O(1) mathematical time.

### Geometry Functions (`geometry.py`)

- **`generate_pythagorean_triples(limit: int) -> List[Tuple[int, int, int]]`**: Generates all Pythagorean triples (a, b, c) where the hypotenuse `c <= limit`.
- **`lattice_points_in_circle(radius_squared: int) -> int`**: Counts the number of integer coordinates (x, y) that fall strictly inside a circle of a given squared radius.
- **`circles_intersect(x1, y1, r1, x2, y2, r2) -> str`**: Evaluates the intersection of two circles. Returns `'CAUGHT'` (overlap), `'DANGER'` (tangent), or `'SAFE'` (separated).

### Boolean Logic (`logic.py`)

- **`evaluate_truth_table(variables: list, expression: str) -> list`**: Generates a complete truth table for a given boolean expression string.
- **`count_true_statements(variables: list, expression: str) -> int`**: Counts how many permutations of the given variables evaluate to `True`.

_(More features may be added in the future!)_

## Installation

You can install HyqerionMath directly from PyPI:

```bash
pip install hyqerionmath
```
