#!/usr/bin/env python
# coding: utf-8

# # Find frequencies that make only $(\hat{a}^2\hat{b}^2\hat{e}^{2}+\hat{a}\hat{b}\hat{d}\hat{e}^{\dagger3})\hat{c}^\dagger +h.c.$ resonant in the 7th order expansion of $\sin(\hat{a}+\hat{b}+\hat{c}+\hat{d}-\hat{e}+h.c.)+\sin(\hat{a}+\hat{b}+\hat{c}-\hat{d}+\hat{e}+h.c.)$

# Proceed as in the 5th order example.

# In[1]:


import hamnonlineng as hnle


# In[2]:


letters = 'abcde'
resonant = [hnle.Monomial(1, 'aabbeeC'), hnle.Monomial(1,'abdEEEC')]
abc_sum = hnle.operator_sum('abc')


# In[3]:


abc_pd_me = abc_sum + hnle.Monomial(1,'d') - hnle.Monomial(1,'e')
abc_md_pe = abc_sum - hnle.Monomial(1,'d') + hnle.Monomial(1,'e')


# In[4]:


sine_exp = (
            hnle.sin_terms(abc_pd_me, 3)
           +hnle.sin_terms(abc_pd_me, 5)
           +hnle.sin_terms(abc_pd_me, 7)
           +hnle.sin_terms(abc_md_pe, 3)
           +hnle.sin_terms(abc_md_pe, 5)
           +hnle.sin_terms(abc_md_pe, 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))


# Try to solve (takes around a minute):

# In[5]:


res = hnle.head_and_count(
        hnle.solve_constraints_gecode(resonant, off_resonant, letters, maxfreq=44))


# Solve it again, but now with linear programming methods and continuous values for the frequencies.

# In[6]:


hnle.solve_linearprog_pulp(resonant, off_resonant, letters, maxfreq=50, detune=1)


# Calculate the detuning of all off-resonant terms and plot a histogram (x: detuning, y: number of terms with that detuning).

# In[7]:


dets = hnle.detuning_of_monomial(res[0], off_resonant, letters)


# In[8]:


get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt


# In[9]:


plt.hist(dets, bins=50, range=(0,50));


# In[10]:


plt.hist(dets, bins=50, range=(0,400));