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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.core.function import Function | |
| from sympy.core.sympify import sympify | |
| from sympy.functions.elementary.hyperbolic import tanh | |
| from sympy.functions.elementary.trigonometric import (cos, sin) | |
| from sympy.series.limits import limit | |
| 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]) | |
| 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]) | |
| 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 | |
| def eval(cls, arg): | |
| arg = sympify(arg) | |
| if arg == 0: | |
| return sympify(0) | |
| e = tanh(x) | |
| f = mytanh(x) | |
| assert e.series(x, 0, 6) == f.series(x, 0, 6) | |