integration can take a _long_ time (possibly forever)

[lxkain]

Hello,

When I do

t = symbols('t', real=True)
def nsinc(t):
    "normalized sinc function"
    return sinc(pi * t)

nsinc(t).integrate()

the process either takes a long time, or doesn't return.

[asmeurer]

It's (unsurprisingly) stuck in the heurisch algorithm.

[rohitrango]

This looks like a good start for something a little more advanced. I have fixed a few easy bugs but I don't feel that I have understood how SymPy works yet. Where should I start to fix this issue (and start learning more about the functioning of the framework) ?

[jksuom]

The integrals module makes use of several integrators which are suited for different kinds of integrands. nsinc can be integrated by meijerint, which can be seen by setting the keyword meijerg:

 In [23]: nsinc(t).integrate(meijerg=True)
Out[23]: 
Si(π⋅t)
───────
   π 

The integration takes a long time because heurisch is attempted before meijerint in the current implementation. (The extra pi in the normalized sinc function makes heurisch particularly sluggish since it then reverts to using polynomial algebra in the very slow expression domain EX. Integrating the unnormalized sinc only takes a reasonable time.)

[asmeurer]

I seem to remember that there was a good reason for it, but why is heurisch tried before meijerg? Heurisch is the slowest and hence ought to be tried last.

[rohitrango]

So, should the ordering of the algorithms be changed? That seems like a better fix than considering special functions separately.

[jksuom]

should the ordering of the algorithms be changed?

Yes, meijerint should come before heurisch. It can integrate many functions that heurisch cannot handle. In those cases no time will be wasted with heurisch.

[rohitrango]

Yes, actually I tried integrating some non common functions and meijerint was able to solve them quicker.