Extending Sympy integration functionalities
Oldřich Klimánek
Hi everyone,
I'd like to follow up on my previous email. I understand the subject line might have discouraged some people—not everyone knows what that means. :) Simply put, my package can solve integrals that Sympy itself cannot handle. It probably doesn't matter what they're called, but on the Sympy Github issues, you can find a lot of reports that Sympy can't solve, for example, the seemingly simple integral of x/(exp(x)-1) from 0 to infinity, or the famous integral in a similar form: x**3/(exp(x)-1).
In [1]: from sympy import symbols, Integral, exp, oo
...: x = symbols('x')
...: I = Integral(x**3 / (exp(x) - 1), (x, 0, oo))
...: I.doit()
Out[1]: Integral(x**3/(exp(x) - 1), (x, 0, oo))
When my package is used, the value of the integral is ready in 1 ms:
In [2]: from bosefermi import bose_fermi_integral
...: bose_fermi_integral(I)
Out[2]: pi**4/15
I would be happy if someone would join me and help with the integration of this package directly into Sympy.
https://github.com/klimanek/Bose-Fermi
Aaron Meurer
patterns is using the manualintegrate module.
https://github.com/sympy/sympy/blob/master/sympy/integrals/manualintegrate.py
Although unfortunately it presently doesn't support definite integrals
so either support for that would need to be added, or you'd need to
find an indefinite form for your integrand using special functions.
The definite form would then ideally be computed automatically using
FTC and the limit() function.
The more complex way, but which might ultimately be a better match for
your integral, is extending the Meijer G-function algorithm. See
https://docs.sympy.org/latest/modules/integrals/g-functions.html
Aaron Meurer
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