Date: Jun 10, 2013 6:22 AM
Author: clicliclic@freenet.de
Subject: Re: The Charlwood Fifty


"Nasser M. Abbasi" schrieb:
>
> I've update the listing of the first 10 integrals. Added your optimal
> results there, and also added result from Sage 5.4.
>
> http://www.12000.org/my_notes/ten_hard_integrals/index.htm
>
> Each integral is now on a separate web page instead of them
> all on the same page to make it easier to see the results
> of each.
>
> There is also a pdf file.
>
> Here is a quick summary of the first 10 integral results,
> I just counted if CAS gave result or not. No checking for
> anything else. Some results are clearly not optimal and
> few results take many pages.
>
> 1. Mathematica: did 1,2,3,4,6,8,9,10 did not: 5,7
> 2. Maple: did 1,2,3,4,5,6,7,8 did not: 9,10
> 3. Rubi4: did 2,3(?),4,5,6,7,8,9,10 did not: 1
> 4. Sage: did: 1,2,3,4,7,9 did not: 5,6,8,10
>
> I do not understand Rubi4 result for 3. I do not know what
> Subst[....] is supposed to mean, but I have not looked it
> up, I am sure it is explained somewhere. Any errors, please
> let me know.
>


I noticed that your MMA and Rubi integrands for problem #7 have and
extra outer root.

I strongly suspect that "Sage" always means "Maxima" (not e.g. "Sympy"):
see the Runtime Error Message for problem #8.

Rubi's SUBST means "substitute": SUBST(a+b,b,c+d) = a+(c+d). Since
Rubi's answer to problem #3 contains an unresolved integral inside the
SUBST statemant, it must be counted as "not done".

Martin.