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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def simplify(self):
 """Simplify the Term."""

        def mul(op1, op2):
            if op1 == "I":
                return 1.0, op2
            if op2 == "I":
                return 1.0, op1
            if op1 == op2:
                return 1.0, "I"
            if op1 == "X":
                return (-1j, "Z") if op2 == "Y" else (1j, "Y")
            if op1 == "Y":
                return (-1j, "X") if op2 == "Z" else (1j, "Z")
            if op1 == "Z":
                return (-1j, "Y") if op2 == "X" else (1j, "X")

        before = defaultdict(list)
        for op in self.ops:
            if op.op == "I":
                continue
            before[op.n].append(op.op)
        new_coeff = self.coeff
        new_ops = []
        for n in sorted(before.keys()):
            ops = before[n]
            assert ops
            k = 1.0
            op = ops[0]
            for _op in ops[1:]:
                _k, op = mul(op, _op)
                k *= _k
            new_coeff *= k
            if new_coeff.imag == 0:
                # cast to float
                new_coeff = new_coeff.real
            if op != "I":
                new_ops.append(pauli_from_char(op, n))
        return Term(tuple(new_ops), new_coeff)