Date: Jul 23, 2013 8:32 PM
Author: daly@axiom-developer.org
Subject: Re: An independent integration test suite

On Tuesday, July 23, 2013 5:41:42 AM UTC-4, Albert Rich wrote:
> On Monday, July 22, 2013 4:33:29 PM UTC-10, da...@axiom-developer.org wrote:
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> > There were a couple of examples where Rubi's answer did not differentiate
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> > to a constant value. These are mentioned in a previous post.
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> Please post the test-suite integrands and their optimal antiderivatives you claim are incorrect, so I can fix the test-suite files if need be.
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> BTW, the optimal antiderivatives in the test-suite are not necessarily "Rubi's answer". Rather, Rubi gets the optimal antiderivative on about 99.8% of the problems in the test-suite.
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> Albert


I updated the first test suite (the files for (a+b x)^m (c+d x)^n).
The abstract for each file contains statistics of interest.

We differ on some results because Rubi (or whatever program you are using
to create the optimal results) assumes that square roots have only a single
positive value. Axiom does not want to make this simplification so given
sqrt(3)*sqrt(7)*sqrt(21) - 21
Axiom will not simplify this to zero but the Rubi test suite does.

Some guys named Jeffrey and Rich published a paper about this many
centuries ago.

Axiom also occasionally complains about non-constant residues, apparently
due to some random constant generation. I will look into it.