Number Theory Library

src/gcd_calculator.py

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+from typing import List, Union
+from math import sqrt
+
+def get_prime_factors(n: int) -> List[int]:
+    """
+    Decompose a number into its prime factors.
+
+    Args:
+        n (int): The number to factorize (must be a positive integer)
+
+    Returns:
+        List[int]: A list of prime factors
+
+    Raises:
+        ValueError: If input is less than 1
+    """
+    if n < 1:
+        raise ValueError("Input must be a positive integer")
+
+    # Handle special cases
+    if n == 1:
+        return [1]
+
+    factors = []
+
+    # Check for 2 as a factor
+    while n % 2 == 0:
+        factors.append(2)
+        n //= 2
+
+    # Check for odd prime factors
+    for i in range(3, int(sqrt(n)) + 1, 2):
+        while n % i == 0:
+            factors.append(i)
+            n //= i
+
+    # If n is a prime greater than 2
+    if n > 2:
+        factors.append(n)
+
+    return factors
+
+def gcd_prime_factors(a: int, b: int) -> int:
+    """
+    Calculate the Greatest Common Divisor (GCD) using prime factorization.
+
+    Args:
+        a (int): First number 
+        b (int): Second number
+
+    Returns:
+        int: The Greatest Common Divisor
+
+    Raises:
+        ValueError: If either input is less than 1
+    """
+    # Handle zero cases
+    if a == 0 and b == 0:
+        return 0
+
+    # Take absolute values to handle negative inputs
+    a, b = abs(a), abs(b)
+
+    # If either number is 0, return the other number
+    if a == 0:
+        return b
+    if b == 0:
+        return a
+
+    # Get prime factors for both numbers
+    a_factors = get_prime_factors(a)
+    b_factors = get_prime_factors(b)
+
+    # Calculate GCD by multiplying common prime factors
+    gcd = 1
+    a_factor_counts = {}
+    b_factor_counts = {}
+
+    # Count occurrences of factors
+    for factor in a_factors:
+        a_factor_counts[factor] = a_factor_counts.get(factor, 0) + 1
+    for factor in b_factors:
+        b_factor_counts[factor] = b_factor_counts.get(factor, 0) + 1
+
+    # Find common factors with minimum count
+    for factor, count in a_factor_counts.items():
+        if factor in b_factor_counts:
+            common_count = min(count, b_factor_counts[factor])
+            gcd *= factor ** common_count
+
+    return gcd

src/prime_checker.py

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+def is_prime(number: int) -> bool:
+    """
+    Check if a given number is prime.
+
+    Args:
+        number (int): The number to check for primality.
+
+    Returns:
+        bool: True if the number is prime, False otherwise.
+
+    Raises:
+        TypeError: If the input is not an integer.
+        ValueError: If the input is less than 2.
+    """
+    # Validate input type
+    if not isinstance(number, int):
+        raise TypeError("Input must be an integer")
+
+    # Handle special cases
+    if number < 2:
+        return False
+
+    # Optimization: check divisibility up to square root of the number
+    for i in range(2, int(number**0.5) + 1):
+        if number % i == 0:
+            return False
+
+    return True

src/prime_factorization.py

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+from typing import List
+
+def prime_factorization(n: int) -> List[int]:
+    """
+    Compute the prime factorization of a given positive integer.
+
+    Args:
+        n (int): The positive integer to factorize.
+
+    Returns:
+        List[int]: A list of prime factors in ascending order.
+
+    Raises:
+        ValueError: If the input is less than 1.
+    """
+    # Validate input
+    if not isinstance(n, int):
+        raise TypeError("Input must be an integer")
+
+    if n < 1:
+        raise ValueError("Input must be a positive integer")
+
+    # Handle special cases
+    if n == 1:
+        return []
+
+    # Prime factorization algorithm
+    factors = []
+
+    # First, handle 2 as a special case to optimize odd number checking
+    while n % 2 == 0:
+        factors.append(2)
+        n //= 2
+
+    # Check for odd prime factors
+    factor = 3
+    while factor * factor <= n:
+        while n % factor == 0:
+            factors.append(factor)
+            n //= factor
+        factor += 2
+
+    # If n is a prime number greater than 2
+    if n > 2:
+        factors.append(n)
+
+    return factors

tests/test_gcd_calculator.py

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+import pytest
+from src.gcd_calculator import gcd_prime_factors, get_prime_factors
+
+def test_get_prime_factors():
+    # Test basic prime factorization
+    assert get_prime_factors(12) == [2, 2, 3]
+    assert get_prime_factors(15) == [3, 5]
+    assert get_prime_factors(7) == [7]
+    assert get_prime_factors(1) == [1]
+
+def test_prime_factors_edge_cases():
+    # Test edge cases
+    with pytest.raises(ValueError):
+        get_prime_factors(0)
+    with pytest.raises(ValueError):
+        get_prime_factors(-5)
+
+def test_gcd_prime_factors():
+    # Test various GCD scenarios
+    assert gcd_prime_factors(48, 18) == 6
+    assert gcd_prime_factors(54, 24) == 6
+    assert gcd_prime_factors(17, 23) == 1  # Coprime numbers
+    assert gcd_prime_factors(0, 5) == 5
+    assert gcd_prime_factors(5, 0) == 5
+    assert gcd_prime_factors(0, 0) == 0
+
+def test_gcd_with_negative_numbers():
+    # Test GCD with negative numbers
+    assert gcd_prime_factors(-48, 18) == 6
+    assert gcd_prime_factors(48, -18) == 6
+    assert gcd_prime_factors(-48, -18) == 6
+
+def test_gcd_large_numbers():
+    # Test large numbers
+    assert gcd_prime_factors(1234567, 7654321) == 1  # Coprime large numbers
+    assert gcd_prime_factors(1000000, 10000) == 10000

tests/test_prime_checker.py

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+import pytest
+from src.prime_checker import is_prime
+
+def test_prime_numbers():
+    """Test known prime numbers"""
+    prime_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+    for prime in prime_numbers:
+        assert is_prime(prime) == True, f"{prime} should be prime"
+
+def test_non_prime_numbers():
+    """Test known non-prime numbers"""
+    non_prime_numbers = [0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22]
+    for non_prime in non_prime_numbers:
+        assert is_prime(non_prime) == False, f"{non_prime} should not be prime"
+
+def test_large_prime():
+    """Test a large prime number"""
+    assert is_prime(104729) == True, "Large prime number not recognized"
+
+def test_large_non_prime():
+    """Test a large non-prime number"""
+    assert is_prime(100000) == False, "Large non-prime number not detected"
+
+def test_negative_numbers():
+    """Test negative numbers"""
+    assert is_prime(-7) == False, "Negative numbers should not be prime"
+
+def test_invalid_input_type():
+    """Test invalid input types"""
+    with pytest.raises(TypeError):
+        is_prime("not a number")
+
+    with pytest.raises(TypeError):
+        is_prime(3.14)
+
+    with pytest.raises(TypeError):
+        is_prime(None)

tests/test_prime_factorization.py

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+import pytest
+from src.prime_factorization import prime_factorization
+
+def test_prime_factorization_basic():
+    assert prime_factorization(12) == [2, 2, 3]
+    assert prime_factorization(15) == [3, 5]
+    assert prime_factorization(100) == [2, 2, 5, 5]
+
+def test_prime_factorization_prime_numbers():
+    assert prime_factorization(7) == [7]
+    assert prime_factorization(11) == [11]
+    assert prime_factorization(17) == [17]
+
+def test_prime_factorization_edge_cases():
+    assert prime_factorization(1) == []
+    assert prime_factorization(2) == [2]
+
+def test_prime_factorization_large_number():
+    result = prime_factorization(84)
+    assert result == [2, 2, 3, 7]
+    assert all(is_prime(factor) for factor in result)
+
+def test_prime_factorization_invalid_inputs():
+    with pytest.raises(ValueError):
+        prime_factorization(0)
+    with pytest.raises(ValueError):
+        prime_factorization(-5)
+    with pytest.raises(TypeError):
+        prime_factorization(3.14)
+    with pytest.raises(TypeError):
+        prime_factorization("not a number")
+
+def is_prime(n: int) -> bool:
+    """Helper function to check if a number is prime."""
+    if n < 2:
+        return False
+    for i in range(2, int(n**0.5) + 1):
+        if n % i == 0:
+            return False
+    return True