Rule-based integration
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From: Albert on 30 Jun 2010 03:12 On Jun 29, 6:45 pm, Vladimir Bondarenko <v...(a)cybertester.com> wrote: > 1) how much time have you spent writing the Rubi? I installed Mathematica 6 on my computer in February 2008, and started learning its pattern-based programming language. By March I was defining integration rules and generating a test suite of problems. By May, I figured out a way to single-step through integration problems, which evolved into a great tool for finding and debugging new rules. > 2) how much time you and your beta testers spent for QA? Until I announced Rubi to the world on this Usenet thread, there were no users or beta-testers. Instead I depend on a comprehensive test suite of problems designed to test every aspect of new rules. It provides an essential "reality check" while developing a rule-based system. So at least 2/3 of my development time is spent adding new problems to the test suite, and then debugging deficiencies exposed. > 3) is there a list of known bugs in the Rubi? Yes, the raw Rubi Test Results are available on the website at http://www.apmaths.uwo.ca/~arich/TestSuiteResults/RubiResults/RubiTestResults.html Finally, I would like to reiterate that Rubi is an open-source system, not intended to be a commercial product (although you are free to incorporate it into such products). Rather it is intended to demonstrate the feasibility and advisability or the rule-based approach to automating mathematics. I look forward to the results produced by the VM Machine, so problems can be added to the test suite and rules can be added to resolve them. Albert
From: Vladimir Bondarenko on 21 Jul 2010 14:21 Your record definitely cries for the Guinness record book application :) As for Rubi, we usually kill the tasks after 100,000 seconds maximally. But often Rubi kills Mathematica quicker. Cheers, Vladimir On Jul 21, 9:08 pm, cliclic...(a)freenet.de wrote: > cliclic...(a)freenet.de schrieb: > > > > > FriCAS has been working on > > > INT(SQRT(SQRT(x^4+1)+x^2)/((x+1)^2*SQRT(x^4+1)),x) > > > for twenty days now! > > FriCAS has been working on > > INT(SQRT(SQRT(x^4+1)+x^2)/((x+1)^2*SQRT(x^4+1)),x) > > for thirty days now! > > Martin.
From: Rob Johnson on 21 Jul 2010 19:28 In article <0477ca60-4932-4253-a460-a0858c6ab36b(a)y4g2000yqy.googlegroups.com>, Vladimir Bondarenko <vb(a)cybertester.com> wrote: >On Jun 4, 6:18 am, Albert <Albert_R...(a)msn.com> wrote: >> I would like to announce the launch of the website >> >> www.apmaths.uwo.ca/RuleBasedMathematics >> >> It is dedicated to dedicated to demonstrating the numerous advantages >> of the rule-based approach to automating mathematics. In systems >> implemented using this approach, rules are expressed as elegant >> mathematical formulas, rather than embedded in conventional program >> code. >> >> As proof-of-concept, I have implemented an efficient and robust Rule- >> based Integrator, nicknamed Rubi. Not only can Rubi compute the >> antiderivative for a broad class of integrands, but the results are >> often significantly superior to those produced by the commercial >> computer algebra systems. >> >> The 1500 or so integration rules Rubi uses are freely available on the >> website in both human and machine readable form. Also available is a >> test suite of over 9400 integration problems developed in conjunction >> with the rules. After reviewing the homepage, I recommend clicking on >> "Highlights of the Indefinite Integration Test Results" for an eye- >> opening comparison of the rule-based integrator (Rubi) with >> Mathematica's and Maple's built-in integrators. >> >> Also if you have access to Mathematica 6 or better, there is a link >> near the bottom of the homepage to download Rubi so you can verify the >> results for yourself. Rubi also provides the option to show the rules >> required to integrate expressions, along with the intermediate >> results. I think this show-step ability has great potential >> pedagogical and research value. >> >> Currently the website is pretty Spartan in format, and limited to >> indefinite integration. However with the help of the computer algebra >> community, I hope it evolves into a true repository of mathematical >> knowledge. >> >> Aloha from Hawaii, >> Albert D. Rich > >There is much to say about the Rubi. > >One tiny example. > >The VM machine says: > >Mathematica 7.0.1.0 returns > > Integrate[1/(Sqrt[2] + Sin[z] + Cos[z]), z] > >unevaluated (!). > >Rubi returns > > -(2/(1 + (-1 + Sqrt[2]) Tan[z/2])) > >which is a correct answer. Integrate[TrigFactor[1/(Sqrt[2] + Sin[z] + Cos[z])], z] gives Pi + 4 z Sqrt[2] Sin[--------] 8 ----------------------------- Pi + 4 z Pi + 4 z Cos[--------] + Sin[--------] 8 8 which is sqrt[2] + 1 greater than the Rubi answer, but still a valid integral. Mathematica has the ability to finish off this integral, but it simply stops too soon. Rob Johnson <rob(a)trash.whim.org> take out the trash before replying to view any ASCII art, display article in a monospaced font
From: Vladimir Bondarenko on 23 Jul 2010 23:00 We bought a dedicated i7-960/12 Gb DDR3 machine for the VM machine to test the Albert Rich's Rubi. http://www.apmaths.uwo.ca/~arich/ Our goal is to see how the human beings compare against the VM machine, so we urge all the interested person to publish the Rubi bugs. Out comment is that the Rubi bug list Albert puts at his site is, to put it mildly, too short. Best wishes, Vladimir Bondarenko VM and GEMM architect Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester, LLC http://maple.bug-list.org/ Maple Bugs Encyclopaedia http://www.CAS-testing.org/ CAS Testing ----------------------------------------------------- "We must understand that technologies like these are the way of the future." ----------------------------------------------------- On Jun 4, 6:18 am, Albert <Albert_R...(a)msn.com> wrote: > I would like to announce the launch of the website > > www.apmaths.uwo.ca/RuleBasedMathematics > > It is dedicated to dedicated to demonstrating the numerous advantages > of the rule-based approach to automating mathematics. In systems > implemented using this approach, rules are expressed as elegant > mathematical formulas, rather than embedded in conventional program > code. > > As proof-of-concept, I have implemented an efficient and robust Rule- > based Integrator, nicknamed Rubi. Not only can Rubi compute the > antiderivative for a broad class of integrands, but the results are > often significantly superior to those produced by the commercial > computer algebra systems. > > The 1500 or so integration rules Rubi uses are freely available on the > website in both human and machine readable form. Also available is a > test suite of over 9400 integration problems developed in conjunction > with the rules. After reviewing the homepage, I recommend clicking on > "Highlights of the Indefinite Integration Test Results" for an eye- > opening comparison of the rule-based integrator (Rubi) with > Mathematica's and Maple's built-in integrators. > > Also if you have access to Mathematica 6 or better, there is a link > near the bottom of the homepage to download Rubi so you can verify the > results for yourself. Rubi also provides the option to show the rules > required to integrate expressions, along with the intermediate > results. I think this show-step ability has great potential > pedagogical and research value. > > Currently the website is pretty Spartan in format, and limited to > indefinite integration. However with the help of the computer algebra > community, I hope it evolves into a true repository of mathematical > knowledge. > > Aloha from Hawaii, > Albert D. Rich
From: Albert on 24 Jul 2010 00:49
On Jul 23, 5:00 pm, Vladimir Bondarenko <v...(a)cybertester.com> wrote: > Out comment is that the Rubi bug list Albert puts > at his site is, to put it mildly, too short. Hello Vladimir, I can't fix the bugs unless you tell me what they are... Albert |