Date: Sep 14, 2013 1:53 PM
Subject: Re: The integration test suites for Sage.
> I now have benchmarked SymPy 0.7.3, which was released
> on July 13, 2013. See the release notes .
> An implementation for SymPy can be found at github .
> The results are listed at .
>  https://github.com/sympy/sympy/wiki/Release-Notes-for-0.7.3
>  https://github.com/PeterLuschny/CharlwoodTest
>  http://luschny.de/math/quad/IntegralTestsSympy.html
Your tests of the SymPy integrator reveal a glaring weakness in the
algebraic arena (most of Charlwood; Timofeev 124, 154-159, 165), and a
lesser one in the rational trigonometric arena (Charlwood 37; Timofeev
108, 114-117, 131, 162). So SymPy's Risch implementation doesn't really
cover trigonometric functions yet. Also Sympy's trigonometric
simplification fails to confirm many valid antiderivatives.
> > PS: How about contributing a chapter of the Timofeev suite yourself?
> Hm, my Russian is a little bit rosty, Genosse Martin!
No knowledge of Russian is needed to copy mathematical expressions from
a 20th century Russian book, and your appeal to comradeship doesn't make
this fact disappear. Some knack for mathematical puzzle solving is
needed, however, to undo any misprints in Timofeev's integrands with the
help of his evaluations. The "examples" for Chapter 5 start near the
bottom of page 202, for integral #4 you turn pages until you reach the
next example section on page 208. Subsequent sections start on pages
211, 213, 219, 223, and so on.
No more flimsy excuses!