Updates:
Labels: WrongResult Integration
Comment #1 on issue 1576 by asmeurer: Integral of strickly positive
function is zero
http://code.google.com/p/sympy/issues/detail?id=1576
What do you have f defined as? You can't have it defined as the default
function from isympy, because I get:
$isympy -c python
Python 2.6.2 console for SymPy 0.6.5
These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z = symbols('xyz')
>>> k, m, n = symbols('kmn', integer=True)
>>> f, g, h = map(Function, 'fgh')
Documentation can be found at http://sympy.org/
>>> fn=Symbol('fn', positive=True)
>>> 4*pi**2*f**2*fn**4*(fn**2+9*f**2)/(fn**2+f**2)**3
Traceback (most recent call last):
File "<console>", line 1, in <module>
TypeError: unsupported operand type(s) for ** or pow(): 'FunctionClass'
and 'int'
By the way, according to Maple, the Maxima result is correct:
> assume(fn, positive);
> 4*pi**2*f**2*fn**4*(fn**2+9*f**2)/(fn**2+f**2)**3;
2 2 4 / 2 2\
4 pi f fn \fn + 9 f /
-------------------------
3
/ 2 2\
\fn + f /
> int(4*pi**2*f**2*fn**4*(fn**2+9*f**2)/(fn**2+f**2)**3,
> f=-infinity..infinity);
2 3
14 pi fn Pi
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