Rubi 2 (Rule-based integrator, version 2)
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From: Vladimir Bondarenko on 11 Aug 2010 01:50 On Aug 11, 6:48 am, Albert <Albert_R...(a)msn.com> wrote: > Version 2 of Rubi (Rule-based integrator) is now available on the > website > > http://www.apmaths.uwo.ca/RuleBasedMathematics > > It consists of 1602 integration rules that can determine the > antiderivative for a wide class of integrands. Precise conditions on > each rule insure it is applied only if doing so makes progress toward > finding an antiderivative. Thus Rubi is algorithmic in nature. It > does not employ heuristic search techniques. > > The following summarizes some of the improvements made since I > announced the website to the sci.math.symbolic Usenet group on 3 June > 2010: > > 1. The integration test suite has expanded to well over 10 thousand > problems. The first version of Rubi is unable to integrate many of > the 1300+ problems added to the test suite. Also the relative > performance of Maple and Mathematica continues to deteriorate as the > test suite gets ever harder and more comprehensive. > > 2. A new category of Contributed problems in the test suite > includes the integration problems in the seminal 1967 PhD thesis > Symbolic Integration by Joel Moses, along with problems recently > submitted by Martin and Vladimir on sci.math.symbolic. If you would > like to contribute indefinite integration problems of reasonable size > and not already in the test suite, I would be happy to include them. > My email address is on the website. > > 3. Many new and fascinating examples comparing the three integrators > in question have been included in the Highlights of the Indefinite > Integration Test Results link. The highlights can now be viewed as > either pdf files or Mathematica notebook files. > > 4. Rubi itself is now delivered as the notebook file Rubi2.nb rather > than a package file. This makes it easier to load and run the system > on various platforms. > > 5. The large increase in trig and hyperbolic function problems in the > test suite reflects the considerable improvements made to Rubi in > response to the issues raised in sci.math.symbolic postings. > > Of particular note is the use of a better algorithm for determining > which trig substitution [sin(x), cos(x), tan(x), cot(x) or tan(x/2)] > to make. Doing so is absolutely essential to avoid going down the > wrong path and ending up with gigantic results. For example, > Mathematica 7 returns a useless result consisting of 277,964 leaves > for the antiderivative of > > cot(x)*sqrt(a+b*cot(x)^2+c*cot(x)^4); > > whereas Rubi 2 returns a valid antiderivative of only 137 leaves by > making the substitution u=cot(x). But not to be outdone, Maple 13 > returns a monster of 9,042,375 leaves for the antiderivative of > > cos(a+b*x)*cot(c+b*x)^3; > > whereas Rubi 2 returns an antiderivative of only 73 leaves. > > The issues raised on sci.math.symbolic played a significant role in > improving Rubi 2, so I look forward to your comments and suggestions. > > Aloha from Hawaii, > Albert Hello Albert, It's nice to see that in the biggest-ever battle for automated mathematics you are at the combat post. Same, me, meaning me as a part of Cyber Tester. In particular, as I mentioned we bought a dedicated i7-960 12 Gb DDR3 based machine for Rubi QA and the VM machine again showed it beats the human beings meaning me and our team members. It is time to announce that a beta 0.1 version of Man+Machine Review Of Rubi had been created some time ago; it is natural, we were waiting for your new release to move further to the beta 0.2 and attached Rubi2 immediately to our machinery. One of the string of questions we pose in the Man+Machine Review Of Rubi, beta 0.1 is how far a human being can move toward the goal of creating of Knowledge Repository without an essential support of some fully automated machinery like the VM machine is. In Rubi2.nb you instruct the user "Extract the contents of the Rubi 2 zip file into a directory of your choice." We extracted it to c:\Rubi2. "To load the integrator without the overhead of the show-stepper, in a fresh instance of Mathematica evaluate the commands : ShowSteps:=False; Get["C:\\Rubi\\UtilityFunctions.m"]; Get["C:\\Rubi\\IntegrationRules.m"]; " (understandable, in our case Rubi should be replaced with Rubi2) which causes Get::noopen: Cannot open C:\Rubi2\IntegrationRules.m. >> as it turns out you changed the filenames of the Rubi set IntegrationRules.m LoadRepository.m ParseFile.m Rubi.m UtilityFunctions.m to IndefiniteIntegrationRules.m LoadRepository.m ParseFile.m Rubi2.nb UtilityFunctions.m which is trivial to fix. So now we run Rubi2... Best wishes from algorithmic Simferopol, Vladimir
From: Albert on 11 Aug 2010 07:05
Hello Vladimir, Thank you for immediately reporting the error in Rubi2.nb. It has been resolved, and a revised version of Rubi 2 is available for downloading from the website. I look forward to the VM machine's assessment of Rubi 2. Albert |