This is the code along with documentation
from sympy import diff, integrate, sympify, expand, Symbol
x=Symbol('x')
def Delta(expr, d = 1):
"""Takes as input function expression and returns the diffrence
between final value(function's expression incremented to 1) and
initial value (function's expression).
>>>from sympy import Symbol
>>>from sympy import sin, cos
>>>from sympy.series.integrals import Delta
>>>x = Symbol('x')
>>>Delta(x**2 + 3*x -2)
2*x + 4
>>>Delta(sin(x))
- sin(x) + sin(x + 1)
If you want an increment different than 1, you can give it the
increment value as an argument to Delta
as shown below
>>>Delta(x**2 - 2*x + 3, 2)
4*x
>>>Delta(x**3 + 3*x**2 + 4*x + 5, 3)
9*x**2 + 45*x + 66
"""
expr=sympify(expr)
a=diff(expr)
b=integrate(a, (x, x, x+d))
expand(b)
return expand(b)
and these are the tests
from sympy import sin, cos
from sympy import pi
from sympy import Symbol
from sympy.series.kauers import Delta
x = Symbol('x', real=True)
m = Symbol('m', real=True)
def test_Delta():
assert Delta(x**2 + 2*x + 1) == 2*x + 3
assert Delta(x**3 + 2*x**2 + 3*x +5) == 3*x**2 + 7*x + 6
assert Delta(x**2 - 2*x + 3) == 2*x - 1
assert Delta(x**2 + 3*x -2) == 2*x + 4
assert Delta(sin(x), pi/6) == -sin(x) + sin(x + pi/6)
assert Delta(cos(x), pi/3)
assert Delta(x**2 - 2*x + 3, 2) == 4*x
assert Delta(x**2 - 2*x + 3, 3) == 6*x + 3
On Jul 8, 7:59 am, Aaron Meurer <[email protected]> wrote:
> It's hard to tell without seeing the code. What you wrote should work.
>
> Aaron Meurer
>
> On Jul 7, 2012, at 5:44 AM, Saurabh Jha <[email protected]> wrote:
>
>
>
>
>
>
>
> > Hi,
>
> > I implemented a Delta() function as a part of my project of
> > implementation of Kauers' algorithm
>
> > It takes as input function expression and returns the difference
> > between final value(function's expression incremented to 1) and
> > initial value (function's expression)
> > .
> > I saved the changes and ran it from sympy at python IDLE as
> > follows
>
> >>>> Delta(x**2 + 2*x + 1)
> > 2*x + 3
>
> > But when I wrote the tests as
>
> > assert Delta(x**2 + 2*x + 1) == 2*x + 3
>
> > it printed assertion error
>
> > The tests diden't passed. I don't know what's the differenece between
> > the two situations, please help me figure it out
>
> > -Saurabh Jha
>
> > --
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