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72 lines
2.0 KiB
72 lines
2.0 KiB
# This test file tests the SymPy function interface, that people use to create
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# their own new functions. It should be as easy as possible.
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from sympy.core.function import Function
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from sympy.core.sympify import sympify
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from sympy.functions.elementary.hyperbolic import tanh
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from sympy.functions.elementary.trigonometric import (cos, sin)
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from sympy.series.limits import limit
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from sympy.abc import x
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def test_function_series1():
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"""Create our new "sin" function."""
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class my_function(Function):
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def fdiff(self, argindex=1):
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return cos(self.args[0])
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@classmethod
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def eval(cls, arg):
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arg = sympify(arg)
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if arg == 0:
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return sympify(0)
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#Test that the taylor series is correct
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assert my_function(x).series(x, 0, 10) == sin(x).series(x, 0, 10)
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assert limit(my_function(x)/x, x, 0) == 1
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def test_function_series2():
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"""Create our new "cos" function."""
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class my_function2(Function):
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def fdiff(self, argindex=1):
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return -sin(self.args[0])
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@classmethod
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def eval(cls, arg):
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arg = sympify(arg)
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if arg == 0:
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return sympify(1)
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#Test that the taylor series is correct
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assert my_function2(x).series(x, 0, 10) == cos(x).series(x, 0, 10)
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def test_function_series3():
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"""
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Test our easy "tanh" function.
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This test tests two things:
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* that the Function interface works as expected and it's easy to use
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* that the general algorithm for the series expansion works even when the
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derivative is defined recursively in terms of the original function,
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since tanh(x).diff(x) == 1-tanh(x)**2
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"""
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class mytanh(Function):
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def fdiff(self, argindex=1):
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return 1 - mytanh(self.args[0])**2
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@classmethod
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def eval(cls, arg):
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arg = sympify(arg)
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if arg == 0:
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return sympify(0)
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e = tanh(x)
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f = mytanh(x)
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assert e.series(x, 0, 6) == f.series(x, 0, 6)
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