Hyper-encoding

#function which calculates the top left of the hypersquare a given index is in
def top_left_hypersquare(variable, length_of_sudoku):
    top_left = [2,2]
    row, column = variable.copy()[0], variable.copy()[1]
    while row > sqrt(length_of_sudoku) + 1:
        row -= sqrt(length_of_sudoku) + 1
        top_left[0] += int(sqrt(length_of_sudoku) + 1)
    while column > sqrt(length_of_sudoku) + 1:
        column -= sqrt(length_of_sudoku) + 1
        top_left[1] += int(sqrt(length_of_sudoku) + 1)
    if row == 1:
        return None
    if column == 1:
        return None
    return top_left

#function which, given two variables, decides if they are in the same hypersquare with
#the same value
def incompatible_hyperBlock(var_1, var_2, length_of_sudoku):
    if var_1 == var_2:
        return False
    if top_left_hypersquare(var_1, length_of_sudoku) == None:
        return False
    if top_left_hypersquare(var_2, length_of_sudoku) == None:
        return False
    if var_1[2] == var_2[2]:
        if top_left_hypersquare(var_1, length_of_sudoku) == top_left_hypersquare(var_2, length_of_sudoku):
            return True
    return False

#function which outputs a list of hypersquare top left coordinates
def generate_top_left_of_hypersquares(length_of_sudoku):
    top_lefts_list = []
    for row in range(2, length_of_sudoku + 1, int(sqrt(length_of_sudoku) + 1)):
        for column in range(2, length_of_sudoku + 1, int(sqrt(length_of_sudoku) + 1)):
            top_lefts_list.append([row, column])
    return top_lefts_list

#function which says every number must appear at least once in each hypersquare
def at_least_hypersquare(length_of_sudoku):
    encoding = []
    for top_lefts in generate_top_left_of_hypersquares(length_of_sudoku):
        for row in range(int(sqrt(length_of_sudoku))):
            for column in range(int(sqrt(length_of_sudoku))):
                encoding.append([])
                for value in range(1, length_of_sudoku + 1):
                    encoding[-1].append(encode_into_number([top_lefts[0] + row, top_lefts[1] + column, value], s_test))
    return encoding

#print(at_least_hypersquare(81))
        
#function which says every number can appear at most once in each hypersquare(NEEDS OPTIMISING)
def at_most_hypersquare(length_of_sudoku):
    encoding = []
    for row in range(1, length_of_sudoku + 1):
        for column in range(1, length_of_sudoku + 1):
            for value in range(1, length_of_sudoku + 1):
                for row2 in range(1, length_of_sudoku + 1):
                    for column2 in range(1, length_of_sudoku + 1):
                        for value2 in range(1, length_of_sudoku + 1):
                            if incompatible_hyperBlock([row, column, value], [row2, column2, value2], length_of_sudoku):
                                encoding.append([-encode_into_number([row, column, value], s_test), -encode_into_number([row2, column2, value2], s_test)])
    return encoding