human
I wrote the below code

    eq = match_['eq']
    func = match_['func']
    fc = match_['func_coeff']
    n = len(eq)
    t = list(list(eq[0].atoms(Derivative))[0].atoms(Symbol))[0]
    constants = numbered_symbols(prefix='C', cls=Symbol, start=1)
    M = Matrix(n, n, (lambda i, j: (- fc[(i, func[j], 0)])))
    evector = M.eigenvects(simplify=True)
    def is_complex(mat, root):
        return Matrix(n, 1, (lambda i, j: ((re(mat[i]) * cos((im(root) * t))) - (im(mat[i]) * sin((im(root) * t))))))
    def is_complex_conjugate(mat, root):
        return Matrix(n, 1, (lambda i, j: ((re(mat[i]) * sin((abs(im(root)) * t))) + (((im(mat[i]) * cos((im(root) * t))) * abs(im(root))) / im(root)))))
    conjugate_root = []
    e_vector = zeros(n, 1)
    for evects in evector:
        if (evects[0] not in conjugate_root):
            if (len(evects[2]) != evects[1]):
                var_mat = Matrix(n, 1, (lambda i, j: Symbol(('x' + str(i)))))
                Mnew = ((M - (evects[0] * eye(evects[2][(-1)].rows))) * var_mat)
                w = [0 for i in range(evects[1])]
                w[0] = evects[2][(-1)]
                for r in range(1, evects[1]):
                    w_ = (Mnew - w[(r - 1)])
                    sol_dict = solve(list(w_), var_mat[1:])
                    sol_dict[var_mat[0]] = var_mat[0]
                    for (key, value) in sol_dict.items():
                        sol_dict[key] = value.subs(var_mat[0], 1)
                    w[r] = Matrix(n, 1, (lambda i, j: sol_dict[var_mat[i]]))
                    evects[2].append(w[r])
            for i in range(evects[1]):
                C = next(constants)
                for j in range((i + 1)):
                    if evects[0].has(I):
                        evects[2][j] = simplify(evects[2][j])
                        e_vector += ((((C * is_complex(evects[2][j], evects[0])) * (t ** (i - j))) * exp((re(evects[0]) * t))) / factorial((i - j)))
                        C = next(constants)
                        e_vector += ((((C * is_complex_conjugate(evects[2][j], evects[0])) *...

What's a good function header?
 Here's a good function header?
assistant
#Here's a good function header.

def _linear_neq_order1_type1(match_):