math_library.py

def scalar_product(vector1, vector2):
    if len(vector1) != len(vector2):
        raise ValueError("Vectors must be of the same length")
    return sum(x * y for x, y in zip(vector1, vector2))

def vector_product(vector1, vector2):
    if len(vector1) != 3 or len(vector2) != 3:
        raise ValueError("Both vectors must be of length 3")
    return [
        vector1[1] * vector2[2] - vector1[2] * vector2[1],
        vector1[2] * vector2[0] - vector1[0] * vector2[2],
        vector1[0] * vector2[1] - vector1[1] * vector2[0]
    ]

def matrix_product(matrix1, matrix2):
    if len(matrix1[0]) != len(matrix2):
        raise ValueError("Number of columns in the first matrix must be equal to the number of rows in the second matrix")
    
    result = [[0 for _ in range(len(matrix2[0]))] for _ in range(len(matrix1))]
    
    for i in range(len(matrix1)):
        for j in range(len(matrix2[0])):
            for k in range(len(matrix2)):
                result[i][j] += matrix1[i][k] * matrix2[k][j]
    
    return result