# sympy/sympy

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 # 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): def fdiff(self, argindex=1): return cos(self.args[0]) @classmethod def eval(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): def fdiff(self, argindex=1): return -sin(self.args[0]) @classmethod def eval(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): def fdiff(self, argindex=1): return 1 - mytanh(self.args[0])**2 @classmethod def eval(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)