The following doctest is disabled pending :trac:`10963`::

                sage: s = SymmetricFunctions(Zmod(14)).s() # not tested
                sage: s.is_integral_domain() # not tested
                False

                    sage: def descent_test(n):
                    ....:     DA = DescentAlgebra(QQ, n)
                    ....:     NSym = NonCommutativeSymmetricFunctions(QQ)
                    ....:     S = NSym.S()
                    ....:     DAD = DA.D()
                    ....:     w_n = DAD(set(range(1, n)))
                    ....:     for I in Compositions(n):
                    ....:         if not (S[I].star_involution()
                    ....:                 == w_n * S[I].to_descent_algebra(n) * w_n):
                    ....:             return False
                    ....:         return True
                    sage: all( descent_test(i) for i in range(4) ) # not tested
                    True
                    sage: all( descent_test(i) for i in range(6) ) # not tested
                    True

                .. TODO::

                    Once :trac:`10963` is in, remove the first "not tested" above,
                    and replace the second one by "long time".