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Topic: The Charlwood Fifty
Replies: 52   Last Post: Jun 24, 2013 10:24 PM

 Messages: [ Previous | Next ]
 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Re: The Charlwood Fifty
Posted: Jun 10, 2013 7:14 AM

On 6/10/2013 5:23 AM, clicliclic@freenet.de wrote:

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

opps, thanks. I just corrected this

http://www.12000.org/my_notes/ten_hard_integrals/index.htm

>
> 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.
>

Ok, the score now looks like this then: (Mathematica gained one, since
it can now do 7, and Rubi4 lost one, since 3 did not count as did)

1. Mathematica: did 1,2,3,4,6,7,8,9,10 did not: 5
2. Maple: did 1,2,3,4,5,6,7,8 did not: 9,10
3. Rubi4: did 2,4,5,6,7,8,9,10 did not: 1,3
4. Sage: did: 1,2,3,4,7,9 did not: 5,6,8,10

btw, Sage 5.4 gives

-1/3 ln(cos(x)^3+1)

for #7 while the optimal result is given as

-2/3 arctanh(sqrt(1+sec(x)^3))

Is the reason the optimal form is prefered over Sage's becuase
it does not contain a log even though Sage answer is smaller in
terms of leaf count?

ps. I used Sage notebook web server http://www.sagenb.org/ versionn
5.4

--Nasser