Date: Sep 15, 2013 8:38 AM
Author: clicliclic@freenet.de
Subject: Re: Rubi 4.1 and the Timofeev test suite


Albert Rich schrieb:
>
> On Tuesday, August 6, 2013 1:51:41 PM UTC-10, clicl...@freenet.de wrote:
>

> > I thought it would be instructive to list those integrals Rubi 4.1 fails on:
> >
> > Timofeev's example 29 from Chapter 1:
> > INT(TAN(x)*TAN(x - a), x)
> > = 1/TAN(a)*LN(1 + TAN(a)*TAN(x)) - x
> >
> > Timofeev's example 64 from Chapter 1:
> > INT(ASIN(x/a)^(3/2)/SQRT(a^2 - x^2), x)
> > = 2/5*ASIN(x/a)^(3/2)*ATAN(x/SQRT(a^2 - x^2))
> > = 2/5*(a/SQRT(a^2 - x^2))*SQRT(1 - (x/a)^2)*ASIN(x/a)^(5/2)
> >
> > Timofeev's example 6 from Chapter 7:
> > INT(x*SIN(x)^3/COS(x)^4, x)
> > = x*(1/(3*COS(x)^3) - 1/COS(x)) - SIN(x)/(6*COS(x)^2) + 5/6*ATANH(SIN(x))
> >
> > Timofeev's example 10 from Chapter 7:
> > INT((2*x + SIN(2*x))/(x*SIN(x) + COS(x))^2, x)
> > = - 2*COS(x)/(x*SIN(x) + COS(x))
> >
> > Timofeev's example 11 from Chapter 7:
> > INT((x/(x*COS(x) - SIN(x)))^2, x)
> > = (x*SIN(x) + COS(x))/(x*COS(x) - SIN(x))
> >
> > In my view, the first two failures are deplorable but understandable,
> > while the third one must be counted as a bug. The last two are simply to
> > be expected.
> >
> > Timofeev's book can be found at:
> >
> > <http://www.math-life.com/jdownloads/view.download/27/279.html>

>
> You probably thought I forgot or ignored your above post. Actually,
> the first three examples inspired me to make significant enhancements
> to the just released version 4.2 of Rubi. In particular, Timofeev's
> example 64 from Chapter 1 resulted in the replacement of an ad hoc
> collection of inverse trig integration rules with a coherent set
> capable of integrating ANY integrable expression of the form
>
> x^m (d+e x^2)^p (a+b arcsin(c x))^n
>
> for any integer (including 0), fraction or symbolic m, n and p; and
> when c^2 d+e=0 (as is the case in example 64) and when not. Rules
> were also defined for analogous expressions involving arccos, arctan
> and arccot; as well as their inverse hyperbolic counterparts. The
> major computer algebra systems are woefully inadequate at integrating
> this difficult class of problems.
>
> Rubi 4.2 gets all the Timofeev examples from Chapters 1, 3 and 7 with
> the exception of #10 and #11 from Chapter 7. So your table of test
> results can be revised to read as follows:
>
> ch. ex's Der. Fri. Mpl MMA Rubi
> 6.10 1.21 17 9 4.2
> -------------------------------------------
> 1 86 83 86 85 86 86
> 2 90 - - - - -
> 3 12 12 12 12 12 12
> 4 132 - - - - -
> 5 120 - - - - -
> 6 26 - - - - -
> 7 11 9 11 11 11 9
> 8 109 - - - - -
> 9 59 - - - - -
> -------------------------------------------
> 100% 95.4% 100% 99.1% 100% 98.2%


Great news! And thanks for the table update. The Winners still are
FriCAS 1.21 and Mathematica 9! (It should be noted that some FriCAS
results do not hold for all values of the integration variable and/or
parameters in the integrand).

>
> I would also like to add the Timofeev examples from the other chapters
> to the Rubi test-suite (currently 44,656 problems). Unfortunately
> when I attempt to follow the above link, I am confronted with the
> unfriendly message "Forbidden: You don’t have permission to access"
> the html file. Any suggestions?


You may try your luck with the hundreds of other sites revealed by the
straightforward Google search (line breaks must be removed before use)

<http://www.google.com/search?q=%D0%A2%D0%B8%D0%BC%D0%BE%D1%84%D0%B5
%D0%B5%D0%B2+%22%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B8%D1%80
%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5+%D1%84%D1%83%D0%BD%D0%BA%D1%86
%D0%B8%D0%B9%22+djvu&hl=en&prmd=ivns&sa=N&btnG=Search>.

Alternatively you may express your need on the newsgroup and will surely
be provided with a copy of the djvu file by one of those who succeeded
in obtaining it earlier (I know that your own need has been satisfied by
now).

Martin.