How to eliminate magic squares formed by the same numbers, but permuted

[Gribouillis]

Add this method to the square class. Then normalize the produced squares and remove repetitions

    def normalize(self):
        if self.mat[0][0] > self.mat[2][2]:
            self.mat = [row[::-1] for row in self.mat[::-1]]
        if self.mat[2][0] > self.mat[0][2]:
            self.mat = [list(row) for row in zip(*self.mat)]
        if self.mat[0][0] > self.mat[2][0]:
            self.mat = self.mat[::-1]

alternately, you can use

def is_magic_and_cool(self):
    return (self.is_magic() and
                self.mat[0][0] < min(self.mat[2][0], self.mat[2][2]) and self.mat[2][0] < self.mat[0][2])

and generate only magic and cool squares.