Python compact matrix Fibonacci

main.py

class FLM:
    iden: int
    step: int

    def sum(self):
        return self.iden + self.step

    def __init__(self, iden = 0, step = 1):
        self.iden = iden
        self.step = step

    def __mul__(self, other):
        step2 = self.step * other.step
        step0 = self.iden * other.iden
        step1 = self.sum() * other.sum() - step0 - step2
        return FLM(step0 + step2, step1 + step2)

    def __str__(self):
        return f"FLM[{self.sum()} {self.step}\n    {self.step} {self.iden}]"

    def __pow__(self, idx):
        ret = FLM(1, 0)
        base = self
        while idx:
            if idx % 2:
                ret *= base
            idx //= 2
            base *= base
        return ret

def fib(n):
    return (FLM() ** n).step