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Pywayne Maths
Mathematical utility functions for factorization, digit counting, and large integer multiplication using Karatsuba algorithm. Use when solving number theory...
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Mathematical utility functions for factorization, digit counting, and large integer multiplication using Karatsuba algorithm. Use when solving number theory...
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Documentation
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
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^logโ3) โ O(n^1.585) More efficient than naive multiplication O(nยฒ) 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
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
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- SKILL.md