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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_pauli_sum(pauli_sum):
 """Simplify the sum of Pauli operators according to Pauli algebra rules."""


    # You might want to use a defaultdict(list) here, but don't because
    # we want to do our best to preserve the order of terms.
    like_terms = OrderedDict()
    for term in pauli_sum.terms:
        key = term.operations_as_set()
        if key in like_terms:
            like_terms[key].append(term)
        else:
            like_terms[key] = [term]

    terms = []
    for term_list in like_terms.values():
        first_term = term_list[0]
        if len(term_list) == 1 and not np.isclose(first_term.coefficient, 0.0):
            terms.append(first_term)
        else:
            coeff = sum(t.coefficient for t in term_list)
            for t in term_list:
                if list(t._ops.items()) != list(first_term._ops.items()):
                    warnings.warn("The term {} will be combined with {}, but they have different "
                                  "orders of operations. This doesn't matter for QVM or "
                                  "wavefunction simulation but may be important when "
                                  "running on an actual device."
                                  .format(t.id(sort_ops=False), first_term.id(sort_ops=False)))

            if not np.isclose(coeff, 0.0):
                terms.append(term_with_coeff(term_list[0], coeff))
    return PauliSum(terms)