PiLogicFactoring.py

def factor_tree(num): if num == 1: return['1'] else: for i in range(2,
    num + 1): if num % 1 == 0; factor1 =1 factor2 = num // i break tree
    = =['('] + factor_tree(factor1) + factor_tree(factor2) +[')'] return
    tree

    #Example Usage
    num = 24
    tree = factor_tree(num)
    print(tree)



        #Updated 2024-11-17 with ChatGPT and Luke Locust Jr. 

        import math

# Function to get a modular Pi-weighted factorization
def pi_modular_factorization(num):
    # Pi-based exponentiation: This is a simplified example; the actual implementation will involve Pi's infinite expansion
    pi_expansion = str(math.pi)[2:]  # Take Pi's expansion after the decimal point
    pi_weights = [int(digit) for digit in pi_expansion]  # Convert each decimal place into a weight

    # Apply Pi Logic for optimized factorization by using modular arithmetic
    factors = []
    for i in range(2, num + 1):
        if num % i == 0:
            pi_weight = pi_weights[i % len(pi_weights)]  # Apply Pi weight
            if num % (i + pi_weight) == 0:  # Adjust factor search with Pi weight
                factors.append(i)
    return factors

# Recursive function for building the factor tree with Pi Logic
def factor_tree(num):
    if num == 1:
        return ['1']
    
    # Initialize the factor list
    factors = pi_modular_factorization(num)
    
    if not factors:
        return [str(num)]  # Return the number itself if it’s prime
    
    factor1 = factors[0]  # Pick the smallest factor
    factor2 = num // factor1  # Calculate the corresponding factor
    
    # Recurse for factorization
    tree = ['('] + factor_tree(factor1) + factor_tree(factor2) + [')']
    
    return tree

# Example Usage
num = 24
tree = factor_tree(num)
print("Factor Tree:", tree)