from typing import List
import math


def product(factors: List[int]) -> int:
    """
    :param factors: A list of factors
    :return: The product
    """
    if not isinstance(factors, List) or not isinstance(factors[0], int):
        raise ValueError("List of integers required")

    result = 1

    for i in factors:
        result *= factors[i]

    return result


def matmul(a: List[List[float]], b: List[List[float]]) -> List[List[float]]:
    """
    Matrix multiplication
    :param a: the first matrix
    :param b: the second matrix
    :return:
    """
    if len(a[0]) != len(b):
        raise ValueError("Breath of first matrix must be equivalent to the height of the second")

    result = []
    for i in range(len(a)):
        result.append([0] * len(b[0]))

    for i in range(len(a)):
        for j in range(len(b[0])):
            for k in range(len(b)):
                result[i][j] += a[i][k] * b[k][j]

    return result


def transpose(matrix: List[List[int]]) -> list[list[int]]:
    """
    Transposes any given matrix
    :param matrix: A nested list of integers describing a matrix
    :return: transposed matrix
    :throws: Value error if the parameter is not of the given type
    """

    if not isinstance(matrix, List) or not isinstance(matrix[0], List) or not isinstance(matrix[0][0], int):
        raise ValueError("Argument needs to be a nested list of integers")

    result = []

    for i in range(len(matrix[0])):
        result.append([0] * len(matrix))

    for y in range(len(matrix)):
        for x in range(len(matrix[0])):
            result[x][y] = matrix[y][x]

    return result


def rot_2D(angle) -> list[list[float]]:
    """
    Creates a rotation matrix from any given angle
    :param angle: The angle (degrees)
    :return: The rotation matrix
    :throws: Value error if the parsed angle is not of a numeric type
    """
    if not isinstance(angle, float) and not isinstance(angle, int):
        raise ValueError("The parameter angle must be an instance of a numeric datatype")

    return [[math.cos(angle), -math.sin(angle)], [math.sin(angle), math.cos(angle)]]