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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Find frequencies that make only $(\hat{a}^2\hat{b}^2\hat{e}^{\dagger2}+\hat{a}\hat{b}\hat{d}^2\hat{e}^{\dagger2})\hat{c}^\dagger +h.c.$ resonant in the 7th order expansion of $\sin(\hat{a}+\hat{b}+\hat{c}+\hat{d}+\hat{e}+h.c.)$
Proceed as in the 5th order example.
Step1:  Try to solve (takes around a minute)
Step2:  Remove constraints on terms of the form $\hat{a}^2\hat{b}^2\dots$ or $\hat{a}\hat{b}\dots$ or those that do not contain any $\hat{a}$s or $\hat{b}$s.
Step3:  Try to solve again
Step4:  See which of the removed constraints fail
Step5:  For the second solution
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Python Code:
import hamnonlineng as hnle
letters = 'abcde'
resonant = [hnle.Monomial(1, 'aabbEEC'), hnle.Monomial(1,'abddEEC')]
op_sum = hnle.operator_sum(letters)
sine_exp = (
            hnle.sin_terms(op_sum, 3)
           +hnle.sin_terms(op_sum, 5)
           +hnle.sin_terms(op_sum, 7)
           )
off_resonant = hnle.drop_single_mode(
                 hnle.drop_definitely_offresonant(
                   hnle.drop_matching(sine_exp.m, resonant)))
off_resonant = list(off_resonant)
print('Number of off-resonant constraints: %d'%len(off_resonant))
Explanation: Find frequencies that make only $(\hat{a}^2\hat{b}^2\hat{e}^{\dagger2}+\hat{a}\hat{b}\hat{d}^2\hat{e}^{\dagger2})\hat{c}^\dagger +h.c.$ resonant in the 7th order expansion of $\sin(\hat{a}+\hat{b}+\hat{c}+\hat{d}+\hat{e}+h.c.)$
Proceed as in the 5th order example.
End of explanation
res = hnle.head_and_count(
        hnle.solve_constraints_gecode(resonant, off_resonant, letters, maxfreq=50))
Explanation: Try to solve (takes around a minute):
End of explanation
# Drop all of the form aabb...
starts_with_aabb = [_ for _ in off_resonant if _.s[4:5].lower() not in 'ab' and _.s.startswith('AABB')]
# Drop all of the form ab...
starts_with_ab   = [_ for _ in off_resonant if _.s[2:3].lower() not in 'ab' and _.s.startswith('AB')]
# Drop all that do not contain any a or b
no_a_or_b = [_ for _ in off_resonant if 'a' not in _.s.lower() or 'b' not in _.s.lower()]
to_be_removed = starts_with_aabb + starts_with_ab + no_a_or_b
print('Number of constraints starting with ab or aabb or containing no a or b: %d'%len(to_be_removed))
off_resonant = hnle.drop_matching(off_resonant, to_be_removed)
off_resonant = list(off_resonant)
print('Number of new off-resonant constraints: %d'%len(off_resonant))
Explanation: Remove constraints on terms of the form $\hat{a}^2\hat{b}^2\dots$ or $\hat{a}\hat{b}\dots$ or those that do not contain any $\hat{a}$s or $\hat{b}$s.
End of explanation
res = hnle.head_and_count(
        hnle.solve_constraints_gecode(resonant, off_resonant, letters, maxfreq=33))
Explanation: Try to solve again:
End of explanation
res[0]
hnle.filter_resonant(res[0], to_be_removed, letters)
Explanation: See which of the removed constraints fail:
For the first solution:
End of explanation
res[1]
hnle.filter_resonant(res[1], to_be_removed, letters)
Explanation: For the second solution:
End of explanation
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