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    Albert D. Rich
    @AlbertRich
    @rfateman Thank you for your interest in Rubi 5. The utility routines needed for the Rubi 5 prototype are defined at the end of its source file in Rubi-5.zip.
    Of course, the number of utility routines will increase as Rubi 5 is fully implemented. However, their implementation should not be that difficult.
    rfateman
    @rfateman
    Looks like Expand, Together, Simplify, polynomial division with remainder are needed. Implementing a substitute for Mathematica's Simplify[] might be a chore. I haven't run (parts of ) Rubi in Lisp recently, or (ever) using Mathematica. I do have a concern that has caused some discussion in the Maxima world. In Maxima there is an attempt to provide an "optimal" solution which has different forms depending on the answers to some questions. e.g. integrate( (ax^2+bx+c)^(3/2),x) can use log or asinh. The current integration program can either use pre-declared assumptions, or asks for the sign of a, whether b is nonzero, and if the discriminant b^2-4ac is zero or not. Interrupting the user with questions is unpopular, especially when the questions are a good deal more complicated! I suppose one could try to answer all questions so as to guide the solution toward the "most generic" answer. I suppose that might include, somehow, all others, even if a far simpler result is sometimes possible. Is there a mechanism to steer Rubi through a potential maze of symbolic inequalities e.g. b^2-4ac > 0 ?? Thanks for keeping up on this project! --RJF
    Albert D. Rich
    @AlbertRich
    @rfateman Rubi does not ask the user questions about the integrand. Rather it always returns mathematically valid antiderivatives in the sense that the derivative of the antiderivative equals the integrand.
    Albert D. Rich
    @AlbertRich

    However to select between antiderivatives which are both valid, Rubi assumes the integrand' s variables are positive. For example, Int[1/Sqrt[a + b x + c x^2], x] returns

    ArcTanh[(b+2*c*x)/(2*Sqrt[c]*Sqrt[a+b*x+c*x^2])]/Sqrt[c]

    whereas Int[1/Sqrt[a + b x - c x^2], x] returns

    -ArcTan[(b-2*c*x)/(2*Sqrt[c]*Sqrt[a+b*x-c*x^2])]/Sqrt[c]

    Note that both results are mathematically valid no matter what nonzero value is substituted for c and both results are free of the imaginary unit if a positive value is substituted for c.

    Albert D. Rich
    @AlbertRich
    @rfateman The Simplify function of the host CAS is not critical to Rubi 5 producing mathematically correct antiderivatives. It only affects how neat and tidy they are.
    Axel Kramer
    @axkr
    @AlbertRich can you comment on this idea please? RuleBasedIntegration/Rubi-5#1
    (Unfortunately we can not see the new issues "on the right" in this gitter chat room. Can you set the link to the repository in the gitter settings to make them appear?)
    Albert D. Rich
    @AlbertRich
    @axkr I commented on your Rubi 5 Issue 1.
    Albert D. Rich
    @AlbertRich
    @axkr I am a novice at Gitter and GitHub. I clicked on "Configure your integrations", then "GitHub" and allowed Gitter to access the RuleBasedIntegration repository. But keep getting an unhelpful error message. What am I doing wrong?
    Miguel Raz Guzmán Macedo
    @miguelraz
    @AlbertRich Congrats! Rubi 5 sounds very, very exciting.
    This open source development you've taken on is impressive and very encouraging, thank you.
    Miguel Raz Guzmán Macedo
    @miguelraz
    Sorry to ask again @AlbertRich, but would you happen to have timings for the test suite for Mathematica vs Rubi?
    SorinS
    @SorinS
    @AlbertRich Very nice start, I like the If-Then idea instead of pattern matching.
    rfateman
    @rfateman
    It's true that the user of symbols a,b,c could have written -a, -b, -c, but the antiderivatives must be valid for any values of a,b,c positive, negative or zero. There is an advantage to some forms of antiderivative which may represent functions continuous in some designated region, as you know. It's a harder problem though, and Rubi's doing great stuff anyway.
    Albert D. Rich
    @AlbertRich
    @rfateman Thanks for your endorsement of Rubi. Note that I said "both results are mathematically valid no matter what nonzero value is substituted for c..." (emphasis added). Neither antiderivative is valid if 0 is substituted for c. Happily the set on which they are invalid (i.e. {0} ) is just a set of measure zero.
    Albert D. Rich
    @AlbertRich

    @miguelraz

    ... would you happen to have timings for the test suite for Mathematica vs Rubi?

    @nasser1 has posted extensive integration test results including performance times for all the major CAS at Computer Algebra Independent Integration Tests.
    Miguel Raz Guzmán Macedo
    @miguelraz
    @AlbertRich Awesome, I think that report was just what I was looking for.
    @nasser1 would you happen to have timing breakdowns by Section? eg Total time taken by a CAS in the Independent tests, Total time taken by a CAS in the Algebraic Binomial tests... so on.
    Miguel Raz Guzmán Macedo
    @miguelraz
    Do those not pass tests?
    Miguel Raz Guzmán Macedo
    @miguelraz
    Also curious what these comments within these Integration rules mean
    Albert D. Rich
    @AlbertRich
    @miguelraz The RuleBasedIntegration/Rubi GitHub repository is not being maintained. Instead to get the most up-to-date Rubi 4 source files, integration test-suite and test results go to the Rule-based Integration website.
    To answer your questions download the relevant Rubi 4 source file as a pdf or notebook file from the Integration Rules page of Rubi's website. Comments in the source files should explain why some code has been commented-out.
    Miguel Raz Guzmán Macedo
    @miguelraz
    Thanks for the prompt response @AlbertRich.
    Ah, manually revising comments in the pdfs is definitely going to hamper part of the translation workflow.
    Oh well :sweat_smile:
    Miguel Raz Guzmán Macedo
    @miguelraz
    Hey @AlbertRich, good news - I've made some headway into the RUBI port to Julia. (Please don't post this link publicly, gimme a week.) I munged all the *.m files in the Rubi rules and dumped them into a huge JSON - this should lessen efforts by others to porting this to their own languages.
    Miguel Raz Guzmán Macedo
    @miguelraz
    Question: I'm now porting the MathematicaSyntaxTestSuite - what are the fields for every entry supposed to mean?
    We have
    {Sqrt[2*x + 1], x, 1, (1/3)*(1 + 2*x)^(3/2)}
    {Sin[x]^3, x, 2, -Cos[x] + Cos[x]^3/3}
    Miguel Raz Guzmán Macedo
    @miguelraz
    Would I be correct in assuming that the
    1. The first field entry Sqrt[2*x + 1] is the expression to integrate
    2. The second field x contains the only variables with respect to integration
    3. The third field 1 contains the "highest level function" the optimal antiderivative may contain (as expressed in the Integration Test Results section)
    4. The fourth field (1/3)*(1 + 2*x)^(3/2) is the answer
    Albert D. Rich
    @AlbertRich
    @miguelraz I say again: To get the most up-to-date Rubi 4 source files, integration test-suite files and test results go to the Rule-based Integration website. For Rubi 5 go to RuleBasedIntegration/Rubi-5.
    Forget the other RuleBasedIntegration repositories on GitHub. As their dates indicate, they are not being maintained.
    Your question about the 4 fields of the integration test-suite files is answered in the first paragraph of the Test Problems page of Rubi's website.
    Miguel Raz Guzmán Macedo
    @miguelraz
    Thanks for the clarification - I had not understood that the Github repositores and the online zip files differ, given that they share the same semantic version of v4.16.1.0. Will update my code accordingly.
    Albert D. Rich
    @AlbertRich
    @miguelraz Sorry about the confusion. Rubi is very much a work-in-progress. Albert
    Miguel Raz Guzmán Macedo
    @miguelraz
    No worries! Your work is paving way for an entire ecosystem for us, so we appreciate all you've done. It really is amazing. If I'm not out of line, do consider bumping the zip file on the Rubi website to 4.17 or akin so that others know it is not the same version as those in the github repos (as is common in semantic versioning practice.)
    Albert D. Rich
    @AlbertRich
    @miguelraz Like I said in the Rubi 5 README file, the next release of Rubi 4 (version 4.17.0) will hopefully be the last. To avoid confusion, I'm starting to think the out-of-date RuleBasedIntegration repositories should all be deleted, or at least hidden...
    Albert D. Rich
    @AlbertRich
    Rather than the collaborative GitHub paradigm, Rubi has pretty much been a one-man show. Its freely available, but read-only, website provides public access to the system. This has given me complete control over Rubi's design and implementation.
    But perhaps Rubi is now mature enough to be transformed into a collaborative software project focused on implementing Rubi 5 and then porting it to popular computer algebra systems. The Plan for Implementing Rubi 5 outlines how this could be achieved as a crowd-source project.
    So if there is sufficient interest, I propose a new repository for Rubi be created and operated as a conventional GitHub site encouraging collaboration (unlike the now dormant RuleBasedIntegration repository).
    Meanwhile, I'll keep my focus on perfecting Rubi 4 to my satisfaction before turning my attention to Rubi 5. So I invite others having the time and inclination, create a repository for The Rubi Project and oversee its operation.
    pretentious7
    @pretentious7
    I'm interested in helping with the sympy implementation and possible future sagemath integration!
    1 reply
    Miguel Raz Guzmán Macedo
    @miguelraz
    @AlbertRich all the more amazing that it's been a one man show!
    I ran into some issues today when parsing the Wester Problems.m - it doesn't share the same structure as the rest of the notebooks.
    Miguel Raz Guzmán Macedo
    @miguelraz
    I also found line 1717 of 1.3.2 Algebraic functions to be malformed:
      1717 (* {Sqrt[1+x^2]/(1-x^3), x, 0} *)