Date: Jun 9, 2013 10:38 PM
Author: Nasser Abbasi
Subject: Re: The Charlwood Fifty
On 6/9/2013 4:58 AM, Albert Rich wrote:

> On Saturday, June 8, 2013 11:12:56 AM UTC-10, clicl...@freenet.de wrote:

>

>> Albert Rich schrieb:

>>

>>> [...] Presumably only a finite number of improvements are possible...

>>

>> Are you sure? [...]

>

> You are severely testing my cherished belief that optimality exists... :=)

>

> I just posted a revised Charlwood Fifty test-suite at

>

> http://www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf

>

> that includes your most recent antiderivatives for problems #41, #42 and #44. Please disregard the 8 previous versions.

>

> Albert

>

fyi;

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.

--Nasser