| 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182 |
- # This test file tests the SymPy function interface, that people use to create
- # their own new functions. It should be as easy as possible.
- #
- # We test that it works with both Function and DefinedFunction. New code should
- # use DefinedFunction because it has better type inference. Old code still
- # using Function should continue to work though.
- from sympy.core.function import Function, DefinedFunction
- 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."""
- for F in [Function, DefinedFunction]:
- class my_function(F):
- 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."""
- for F in [Function, DefinedFunction]:
- class my_function2(F):
- 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
- """
- for F in [Function, DefinedFunction]:
- class mytanh(F):
- 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 e.series(x, 0, 6) == f.series(x, 0, 6)
|
