from typing import List
import math
from tabulate import tabulate

def matmul(mat1: List[List[int]], mat2: List[List[int]]) -> List[List[int]]:
    """
    Multiplies two matrices and returns the resulting matrix.

    :param mat1: The first matrix
    :param mat2: The second matrix
    :return: A new matrix representing the product of mat1 and mat2
    :raises ValueError: If the number of columns in mat1 does not equal the number of rows in mat2
    """
    if len(mat1[0]) != len(mat2):
        raise ValueError("Matrix isnt computable")

    mat3: List[List[int]] = []
    for i in range(len(mat1)):
        new_row: List[int] = []
        for j in range(len(mat2[0])):
            summe = 0
            for k in range(len(mat2)):
                summe += mat1[i][k] * mat2[k][j]
            new_row.append(summe)
        mat3.append(new_row)
    return mat3


def transpose(matrix: List[List[int]]) -> List[List[int]]:
    """
    Transposes a given matrix (rows become columns and columns become rows).

    :param matrix: A list of lists representing the matrix.
    :return: A new matrix that is the transpose of the input matrix.
    """
    if not matrix:
        raise ValueError("Matrix is empty")

    row_length = len(matrix[0])
    if any(len(row) != row_length for row in matrix):
        raise ValueError("Matrix rows have uneven lengths")

    transposed: List[List[int]] = []
    for i in range(row_length):
        new_row = []
        for j in range(len(matrix)):
            new_row.append(matrix[j][i])
        transposed.append(new_row)
    return transposed


def rot_2D(theta: float) -> List[List[float]]:
    """
    Returns a 2D rotation matrix for a given angle in radians.

    The rotation matrix can be used to rotate points in the 2D plane
    around the origin by the angle theta (counterclockwise).

    :param theta: The rotation angle in radians.
    :return: A 2x2 rotation matrix as a list of lists.
    """
    cos_t = math.cos(theta)
    sin_t = math.sin(theta)
    return [
        [cos_t, -sin_t],
        [sin_t,  cos_t]
    ]


def main():
    # Test matrix multiplication
    matrix_a = [[3, 4, -1, 4],
                [-2, 2, 5, 1]]

    matrix_b = [[1, 3, -2],
                [2, 5, 1],
                [-1, 4, -4],
                [2, 3, 6]]

    matrix_c = matmul(matrix_a, matrix_b)
    print("Ergebnis C = A * B:")
    for row in matrix_c:
        print(row)

    # Test transpose
    matrix = [[1, 2, 3],
              [4, 5, 6]]
    print("\nTransposed:")
    for row in transpose(matrix):
        print(row)

    # Test rotation
    print("\nRotation matrix for 90° (pi/2 radians):")
    for row in rot_2D(math.pi / 2):
        print(row)

    print("Matrix A:")
    print(tabulate(matrix_a))


if __name__ == "__main__":
    main()