pywayne-maths

Pywayne Maths

Mathematical utility functions for number theory, digit analysis, and optimized integer operations.

Quick Start

from pywayne.maths import get_all_factors, digitCount, karatsuba_multiplication

# Get all factors of a number
factors = get_all_factors(28)
print(factors)  # [1, 2, 4, 7, 14, 28]

# Count digit occurrences
count = digitCount(100, 1)
print(count)  # 21 (digit 1 appears 21 times in 1-100)

# Large integer multiplication
product = karatsuba_multiplication(1234, 5678)
print(product)  # 7006652

Functions

get_all_factors

Return all factors of a positive integer.

get_all_factors(n: int) -> list

Parameters:

• n - Positive integer to factorize

Returns:

• List of all factors of n

Use Cases:

• Number theory problems
• Finding divisors
• Simplifying fractions
• Greatest common divisor (GCD) calculation

Example:

from pywayne.maths import get_all_factors

factors = get_all_factors(36)
print(factors)  # [1, 2, 3, 4, 6, 9, 12, 18, 36]

# Check if number is prime
n = 17
factors = get_all_factors(n)
if len(factors) == 2:  # Only 1 and itself
    print(f"{n} is prime")
else:
    print(f"{n} is not prime")

digitCount

Count occurrences of digit k from 1 to n.

digitCount(n, k) -> int

Parameters:

• n - Positive integer, upper bound of counting range
• k - Digit to count (0-9)

Returns:

• Count of digit k in range [1, n]

Special Case:

• When k = 0, counts all numbers with trailing zeros after n

Use Cases:

• Digit frequency analysis
• Number theory problems
• Data analysis tasks

Example:

from pywayne.maths import digitCount

# Count digit 1 from 1 to 100
count = digitCount(100, 1)
print(count)  # 21

# Count each digit 0-9 in range 1-1000
for k in range(10):
    count = digitCount(1000, k)
    print(f"Digit {k}: {count} times")

karatsuba_multiplication

Multiply two integers using Karatsuba's divide-and-conquer algorithm.