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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 phase_transformation(Ne, Nl, rm, xi, return_equations=False):
 """Returns a phase transformation theta_i. The phase transformation is defined in a way such that theta1 + omega_level1 = 0. [-omega_1, -omega_1 - varpi_1] """

    # We first define the needed variables
    E0, omega_laser = define_laser_variables(Nl)
    theta = [Symbol('theta'+str(i+1)) for i in range(Ne)]

    # We check for the case of xi being a list of matrices.
    if type(xi) == list:
        xi = np.array([[[xi[l][i, j]
                       for j in range(Ne)] for i in range(Ne)]
                       for l in range(Nl)])

    # We find all the equations that the specified problem has to fulfil.
    eqs = []
    for i in range(Ne):
        for j in range(0, i):
            if (rm[0][i, j] != 0) or \
               (rm[1][i, j] != 0) or \
               (rm[2][i, j] != 0):
                for l in range(Nl):
                    if xi[l, i, j] == 1:
                        eqs += [-omega_laser[l] + theta[j] - theta[i]]

    if return_equations:
        return eqs

    # We solve the system of equations.
    sol = sympy.solve(eqs, theta, dict=True)
    sol = sol[0]
    # We add any missing theta that may be left outside if the system is
    # under determined.

    extra_thetas = []
    for i in range(Ne):
        if theta[i] not in sol.keys():
            sol.update({theta[i]: theta[i]})
            extra_thetas += [theta[i]]

    # We make the solution such that theta1 + omega_level1 = 0.
    omega_level, omega, gamma = define_frequencies(Ne)
    eq_crit = sol[theta[0]] + omega_level[0]
    ss = sympy.solve(eq_crit, extra_thetas[0])[0]
    ss = {extra_thetas[0]: ss}

    sol_simple = [sol[theta[i]].subs(ss)
                  for i in range(Ne)]

    # sol = []
    # for i in range(Ne):
    #     soli = []
    #     for l in range(Nl):
    #         soli += [sympy.diff(sol_simple[theta[i]], omega_laser[l])]
    #     sol += [soli]

    return sol_simple