On Nov 23, 2008, at 2:34 AM, Robert Bradshaw wrote:
>
> I only know a tiny bit about symbolic integration, but mabshoff's
> statement that it will be a long path is certainly an understatement.
> What I would like to see happen soon is some of the basic cases
> solved in our own code, and then passing off to some other library
> for the harder cases. Sage isn't about about re-inventing the wheel,
> and I hope that something like SymPy will become mature enough to
> handle all the really complicated stuff. In any case the bottleneck
> of pexpect is not as important for the "hard" cases (though perhaps
> the difficulty of building dependancies like lisp is good motivation
> to have more native code).
>
> That being said, if someone does write a full symbolic integration
> suite natively in Sage, that would be great.

Oh, I realize that it's definitely hard. However, while it's certainly
true that Sage isn't about re-inventing the wheel, the pexpect overhead
can be big, especially when you're trying to evaluate many integrals.
Even in my Maple code, I actually go through a fair bit of extra work
to avoid extra integration calls. I'm looking at integrating terms in
a finite element matrix. Since I have symmetry, I only have to do  
half. Each
term doesn't take long to integrate since they're products of  
polynomials,
but they add up, especially when you're working in 3D.

I certainly have quite an interest in this area, so I'd appreciate any
references people might suggest. Not that I'm saying I'd tackle this,
but I'd like to learn more.

Cheers,

Tim.

---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo

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