Integrate in sympy doesn't work for x*cos(n*pi*x/L), but DOES work for sqrt(1.)*x*cos(n*pi*x/L). Please see code snippets below

Question

Code snippet 1:

from sympy import symbols, integrate, cos, pi
from numpy import sqrt
n = symbols('n', integer=True)
x, L = symbols('x L', real=True)
fs_coeff = integrate(sqrt(1.)*x*cos(n*pi*x/L), (x, 0, L))
print fs_coeff

And I get:

-1.0*Piecewise((0, n == 0), (0.101321183642338*L*2/n*2, True)) + 1.0*Piecewise((L**2/2, n == 0), (0.318309886183791*L**2*sin(3.14159265358979*n)/n + 0.101321183642338*L**2*cos(3.14159265358979*n)/n**2, True))

Code snippet 2:

from sympy import symbols, integrate, cos, pi
from numpy import sqrt
n = symbols('n', integer=True)
x, L = symbols('x L', real=True)
fs_coeff = integrate(x*cos(n*pi*x/L), (x, 0, L))
print fs_coeff

And I get an error:

Traceback (most recent call last):

File "test-sympy.py", line 6, in

fs_coeff = integrate(x*cos(n*pi*x/L), (x, 0, L))

...

ValueError: too many values to unpack

I'm using the latest Enthought Canopy python distribution, v. 1.3. Python version 2.7.6, SymPy 0.7.3.

If you have any insight on this, I'd appreciate it.

Answer 1

SymPy 0.7.3 is not the newest version. Try it in 0.7.4.1. This was a bug that has been fixed.

>>> fs_coeff = integrate(x*cos(n*pi*x/L), (x, 0, L))
>>> fs_coeff
Piecewise((L**2/2, n == 0), ((-1)**n*L**2/(pi**2*n**2) - L**2/(pi**2*n**2), True))

Answer 2

The problem seems to be in the handling of the piecewise interval for n=0, which breaks when exact math is being used, but not with approximate math. The sqrt is not necessary, you can get the same result with 1.*x*cos(n*pi*x/L). Since it is unlikely you want n=0, you can get a nice clean answer by limiting n to being positive:

from sympy import symbols, integrate, cos, pi
from numpy import sqrt
n = symbols('n', integer=True, positive=True)
x, L = symbols('x L', real=True)
fs_coeff = integrate(x*cos(n*pi*x/L), (x, 0, L))
print fs_coeff