hyqerionmath 0.5.0

A Python library with mathematical utilities: primality testing, factorization, sequence generation, boolean logic, and coordinate geometry.

HyqerionMath

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:

pip install hyqerionmath