error with python sympy computing integral for cosine function

Question

So I was trying an example directly from the sympy documentation and I am getting a strange error. I am using python 3.2 with sympy 0.7.3. I have been working in the ipython notebook, though I don't think that should make a difference. The error is that whenever I create a "x" symbol and try to integrate the math.cos(x), I get an error saying "can't convert expression to float."

Here is a code example. This is taken from the sympy documentation.

import sympy
import math
x = sympy.Symbol('x')
sympy.integrate(x**2 * math.exp(x) * math.cos(x), x)

The error message that results is:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-123-84e55454fb60> in <module>()
----> 1 sympy.integrate(x**2 * math.exp(x) * math.cos(x), x)

/usr/local/lib/python3.2/dist-packages/sympy/core/expr.py in __float__(self)
242         if result.is_number and result.as_real_imag()[1]:
243             raise TypeError("can't convert complex to float")
--> 244         raise TypeError("can't convert expression to float")
245 
246     def __complex__(self):

TypeError: can't convert expression to float

Any suggestions would be appreciated.

Answer 1

You cannot mix the symbolic mathematical expressions created by the sympy library with normal functions that just calculate a value (like the ones from the math library. If you're creating a symbolic expression, you should always use the sympy functions (sympy.exp, sympy.cos, sympy.log, etc.):

x = sympy.Symbol('x')
sympy.integrate(x**2 * sympy.exp(x) * sympy.cos(x), x)

Operators such as *, +, -... Are overloaded by objects in the sympy library so you can use them in your expressions, but you cannot use normal functions that directly calculate values.