How to evaluate integrals numerically: convert expression to float

[Carlos Bouthelier Madre]

Hi, I am trying to compute an integral of a function f that has no primitive, I have used Integral(f,(Tita1, 0, pi/2).(Tita2,0,pi/2)), because I wanted to be able to define it and operate with it before evaluating it. The problem is that when I try to use .evalf(), it won't give me a float number, just an expression of the integral divided in several sums of the same integral within different intervals. 

The expression of the integral is 

ZE=16.0*Integral(4*Integral(8.0*(194.818182068005*(-sqrt(0.25*cos(Tita1)**2 + 1) + sqrt(0.25*cos(Tita2)**2 + 1))*(sqrt(0.25*cos(Tita1)**2 + 1) + sqrt(0.25*cos(Tita2)**2 + 1))*exp(1.5*sqrt(0.25*cos(Tita1)**2 + 1) - 0.5*sqrt(0.25*cos(Tita2)**2 + 1)) - 194.818182068005*(sqrt(0.25*cos(Tita1)**2 + 1) - sqrt(0.25*cos(Tita2)**2 + 1))**2*exp(0.5*sqrt(0.25*cos(Tita1)**2 + 1) - 0.5*sqrt(0.25*cos(Tita2)**2 + 1)) + 194.818182068005*(sqrt(0.25*cos(Tita1)**2 + 1) - sqrt(0.25*cos(Tita2)**2 + 1))**2*exp(1.5*sqrt(0.25*cos(Tita1)**2 + 1) + 0.5*sqrt(0.25*cos(Tita2)**2 + 1)) + 194.818182068005*(sqrt(0.25*cos(Tita1)**2 + 1) - sqrt(0.25*cos(Tita2)**2 + 1))*(sqrt(0.25*cos(Tita1)**2 + 1) + sqrt(0.25*cos(Tita2)**2 + 1))*exp(0.5*sqrt(0.25*cos(Tita1)**2 + 1) + 0.5*sqrt(0.25*cos(Tita2)**2 + 1)))*exp(-1.0*sqrt(0.25*cos(Tita1)**2 + 1))/((sqrt(0.25*cos(Tita1)**2 + 1) - sqrt(0.25*cos(Tita2)**2 + 1))**2*(sqrt(0.25*cos(Tita1)**2 + 1) + sqrt(0.25*cos(Tita2)**2 + 1))*sqrt(0.25*cos(Tita1)**2 + 1)*sqrt(0.25*cos(Tita2)**2 + 1)), (Tita1, 0, 1.5707963267949)), (Tita2, 0, 1.5707963267949))

What could I use to evaluate it ? How could I define it to make it work? 

In fact, I have substituted some other variables in the expression of ZE, so it can compute the Integral. It would also be useful to know how to plot ZE(x), if x was the unsubstitude variable inside the previous integral.

Thanks in advance

[Aaron Meurer]

Looks like a bug. evalf() should work. Can you open an issue for it in
the SymPy issue tracker?

Aaron Meurer

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[Carlos Bouthelier Madre]

Done, if you meant here: https://github.com/sympy/sympy/issues/12646

How could I fix this bug? Shall I update my sympy version or recover a previous one?

[Carlos Bouthelier Madre]

Hi Aaron,

May the issue be due to the fact that the integral that I am trying to perform is 2 dimensional? Perhaps Integral() doesn't work for more than one variable, and therefore evalf() can't evaluate it and leaves it as an expression. Any ideas for solving it? Shall I use another integration function from another library (scipy or numpy)?

El martes, 16 de mayo de 2017, 20:58:53 (UTC+2), Aaron Meurer escribió: