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BytesAgain β€Ί Skills β€Ί Pywayne Maths
πŸ¦€ ClawHub

Pywayne Maths

by @wangyendt

Mathematical utility functions for factorization, digit counting, and large integer multiplication using Karatsuba algorithm. Use when solving number theory...

Versionv0.1.0
Downloads811
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TERMINAL
clawhub install maths

πŸ“– About This Skill

name: pywayne-maths description: Mathematical utility functions for factorization, digit counting, and large integer multiplication using Karatsuba algorithm. Use when solving number theory problems, computing factors, counting digit occurrences, or performing optimized large integer multiplication.

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.

    karatsuba_multiplication(x: int, y: int) -> int

    Parameters:

  • x - Integer multiplier
  • y - Integer multiplicand

    • Returns:

  • Product of x and y

    • Algorithm:

  • Karatsuba algorithm uses recursive divide-and-conquer to multiply large integers
  • Time complexity: O(n^logβ‚‚3) β‰ˆ O(n^1.585)
  • More efficient than naive multiplication O(nΒ²) for very large numbers

    • Use Cases:

  • Large integer multiplication
  • Algorithm optimization
  • Competitive programming
  • Cryptography applications

    • Example: 

    from pywayne.maths import karatsuba_multiplication
    Compare with standard multiplication
    
a, b = 123456789, 987654321
result = karatsuba_multiplication(a, b)
print(result)  # 121932631112635269
    Verify
    
assert result == a * b

    Common Applications

    Prime Number Detection

    from pywayne.maths import get_all_factors
    def is_prime(n):
    factors = get_all_factors(n)
    return len(factors) == 2 and factors == [1, n]
    print(is_prime(17))   # True
print(is_prime(18))   # False

    Greatest Common Divisor (GCD)

    from pywayne.maths import get_all_factors
    def gcd(a, b):
    factors_a = set(get_all_factors(a))
    factors_b = set(get_all_factors(b))
    common = factors_a & factors_b
    return max(common)
    print(gcd(24, 36))  # 12

    Digit Frequency Analysis

    from pywayne.maths import digitCount
    def digit_frequency(n):
    frequency = {}
    for k in range(10):
        frequency[k] = digitCount(n, k)
    return frequency
    print(digit_frequency(1000))

    {0: 189, 1: 301, 2: 300, 3: 300, ...}

    Large Number Calculations

    from pywayne.maths import karatsuba_multiplication
    Very large numbers
    
x = 123456789012345678901234567890
y = 9876543210987654321098765432109876
    Use Karatsuba for efficiency
    
product = karatsuba_multiplication(x, y)

    Notes

  • get_all_factors returns sorted unique factors
  • digitCount counts from 1 to n inclusive
  • karatsuba_multiplication is optimized for large integers (hundreds+ of digits)
  • For small integers, standard multiplication * may be faster due to overhead

    • πŸ’‘ Examples

    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

    πŸ“‹ Tips & Best Practices

  • get_all_factors returns sorted unique factors
  • digitCount counts from 1 to n inclusive
  • karatsuba_multiplication is optimized for large integers (hundreds+ of digits)
  • For small integers, standard multiplication * may be faster due to overhead