73 lines
2.0 KiB
Python
73 lines
2.0 KiB
Python
|
# 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])
|
||
|
|
|
||
|
|
@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 e.series(x, 0, 6) == f.series(x, 0, 6)
|