Tips for Symbolic Integration of Rational Functions?

asked 2021-05-09 00:03:28 +0200

Ogrelord gravatar image

I am doing some work that requires me to do a lot of symbolic integration of rational functions over the interval [-1, 1]. These rational functions end up containing the integration variable, plus a few real symbolic parameters t1,...,tn. The issue is, as I add more parameters and things get more complicated, Sage's integrate function slows down a lot, and even occasionally seems to get completely stuck.

I am reasonably new to Sage, and my code is able to handle the simpler cases, so it might just be that these functions become too complicated to integrate as I add more parameters. But I'm wondering, are there any general things I could do that might make the integration a little easier/faster? For example, I tried calling .partial_fractions() on the integrand before passing it to the integrate function, but I didn't really notice much of an effect. If you can think of anything that might help speed up these computations, I would appreciate it.

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