# This test file tests the SymPy function interface, that people use to create

 # their own new functions. It should be as easy as possible.

 from sympy import Function, sympify, sin, cos, limit, tanh

 from sympy.abc import x

 def test_function_series1():

     """Create our new "sin" function."""

     class my_function(Function):

         nargs = 1

         def fdiff(self, argindex = 1):

             return cos(self.args[0])

         @classmethod

         def canonize(cls, arg):

             arg = sympify(arg)

             if arg == 0:

                 return sympify(0)

     #Test that the taylor series is correct

     assert my_function(x).series(x, 0, 10) == sin(x).series(x, 0, 10)

     assert limit(my_function(x)/x, x, 0) == 1

 def test_function_series2():

     """Create our new "cos" function."""

     class my_function2(Function):

         nargs = 1

         def fdiff(self, argindex = 1):

             return -sin(self.args[0])

         @classmethod

         def canonize(cls, arg):

             arg = sympify(arg)

             if arg == 0:

                 return sympify(1)

     #Test that the taylor series is correct

     assert my_function2(x).series(x, 0, 10) == cos(x).series(x, 0, 10)

 def test_function_series3():

     """

     Test our easy "tanh" function.

     This test tests two things:

       * that the Function interface works as expected and it's easy to use

       * that the general algorithm for the series expansion works even when the

         derivative is defined recursively in terms of the original function,

         since tanh(x).diff(x) == 1-tanh(x)**2

     """

     class mytanh(Function):

         nargs = 1

         def fdiff(self, argindex = 1):

             return 1-mytanh(self.args[0])**2

         @classmethod

         def canonize(cls, arg):

             arg = sympify(arg)

             if arg == 0:

                 return sympify(0)

     e = tanh(x)

     f = mytanh(x)

     assert tanh(x).series(x, 0, 6) == mytanh(x).series(x, 0, 6)