docs: def linear_get_coefficients(coef, rhouv, s, i, j, k, u, v,
                              unfolding, matrix_form):
      r"""Get the indices mu, nu, and term coefficients for linear terms.
  
      We determine mu and nu, the indices labeling the density matrix components
            d rho[mu] /dt = sum_nu A[mu, nu]*rho[nu]
      for this complex and rho_u,v.
  
      >>> from fast.symbolic import define_density_matrix
      >>> Ne = 2
      >>> coef = 1+2j
      >>> rhouv = define_density_matrix(Ne)[1, 1]
      >>> s, i, j, k, u, v = (1, 1, 0, 1, 1, 1)
      >>> unfolding = Unfolding(Ne, real=True, normalized=True)
  
      >>> linear_get_coefficients(coef, rhouv, s, i, j, k, u, v,
      ...                              unfolding, False)
      [[1, 0, -2.00000000000000, False, False]]
  
      """
      Ne = unfolding.Ne
      Mu = unfolding.Mu
      # We determine mu, the index labeling the equation.
      mu = Mu(s, i, j)
  
      if unfolding.normalized and u == 0 and v == 0:
          # We find the nu and coefficients for a term of the form.
          # coef*rho_{00} = coef*(1-sum_{i=1}^{Ne-1} rho_{ii})
          if unfolding.real:
              ss = 1
          else:
              ss = 0
  
          mu11 = Mu(ss, 1, 1)
          muNeNe = Mu(ss, Ne-1, Ne-1)
          rhouv_isconjugated = False
          if s == 1:
              coef_list = [[mu, nu, im(coef), matrix_form, rhouv_isconjugated]
                           for nu in range(mu11, muNeNe+1)]
          elif s == -1:
              coef_list = [[mu, nu, -re(coef), matrix_form, rhouv_isconjugated]
                           for nu in range(mu11, muNeNe+1)]
          elif s == 0:
              coef_list = [[mu, nu, -coef, matrix_form, rhouv_isconjugated]
                           for nu in range(mu11, muNeNe+1)]
          return coef_list
  
      #####################################################################
  
      if (unfolding.lower_triangular and
         isinstance(rhouv, sympy.conjugate)):
          u, v = (v, u)
          rhouv_isconjugated = True
      else:
          rhouv_isconjugated = False
      # If the unfolding is real, there are two terms for this
      # component rhouv of equation mu.
      if unfolding.real:
          nur = Mu(1, u, v)
          nui = Mu(-1, u, v)
      else:
          nu = Mu(0, u, v)
      #####################################################################
      # We determine the coefficients for each term.
      if unfolding.real:
          # There are two sets of forumas for the coefficients depending
          # on whether rhouv_isconjugated.
          # re(I*x*conjugate(y)) = -im(x)*re(y) + re(x)*im(y)
          # re(I*x*y)            = -im(x)*re(y) - re(x)*im(y)
          # im(I*x*conjugate(y)) = +re(x)*re(y) + im(x)*im(y)
          # im(I*x*y)            = +re(x)*re(y) - im(x)*im(y)
          if s == 1:
              # The real part
              if rhouv_isconjugated:
                  coef_rerhouv = -im(coef)
                  coef_imrhouv = re(coef)
              else:
                  coef_rerhouv = -im(coef)
                  coef_imrhouv = -re(coef)
          elif s == -1:
              if rhouv_isconjugated:
                  coef_rerhouv = re(coef)
                  coef_imrhouv = im(coef)
              else:
                  coef_rerhouv = re(coef)
                  coef_imrhouv = -im(coef)
  
          coef_list = [[mu, nur, coef_rerhouv, matrix_form, rhouv_isconjugated]]
          if nui is not None:
              coef_list += [[mu, nui, coef_imrhouv,
                             matrix_form, rhouv_isconjugated]]
      else:
          coef_list = [[mu, nu, coef, matrix_form, rhouv_isconjugated]]
  
      return coef_list