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.