Where communities thrive


  • Join over 1.5M+ people
  • Join over 100K+ communities
  • Free without limits
  • Create your own community
People
Activity
    Nasser M. Abbasi
    @nasser1
    opps typo above, I meant using Rubi version 4.16.1 and not 14.6.1
    Albert D. Rich
    @AlbertRich
    @nasser1 The Mathematica command Length[DownValues[Int]] returns 6881 Int rules for Rubi 4.16.1.
    Nasser M. Abbasi
    @nasser1

    @AlbertRich Thanks. That works. Do you know why when I print the rules using the following, it shows always as Removed[Int] in there and not just Int? Here is an example

    $LoadShowSteps = False;
     << Rubi`
     BeginPackage["Rubi`"];
     Begin["`Private`"];
     Do[
         Print[InputForm[DownValues[Int][[n]]]]
        ,
         {n, 1, 1}(*Length[DownValues[Int]]}*)
      ]

    Which gives

    HoldPattern[Removed["Int"][(u_.)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol]] :> Removed["Int"][u*(b*x^n)^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[a, 0]

    Now I remove this as follows

      BeginPackage["Rubi`"];
      Begin["`Private`"];
      Do[
          res = InputForm[DownValues[Int][[n]]];
          res = ToString[ReleaseHold[res]];
          res = StringReplace[res, "Defer[Removed[\"Int\"]]" -> "Int"];
          res = StringReplace[res, "Removed[\"Int\"]" -> "Int"];
          Print[res]
           ,
            {n, 1, 1}(*Length[DownValues[Int]]}*)
           ]

    Which gives

    Int[(u_.)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[u*(b*x^n)^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[a, 0]

    Starting from clean Kernel did not help. The Removed[Int] is always there. It is not big deal as I can remove it, this is for just printing the rules, but I wondered why it happens.

    tringocao
    @tringocao
    image.png
    Why WildCards have option S(1)? Can you help me to explain that?
    Anixx
    @Anixx
    I would be glad if anyone commented on my work, particularly, the code that allows to multiply divergent integrals. Here is my post with a Mathematica code, it is like a calculator that allows to multiply two divergent integrals: https://mathoverflow.net/q/421354/10059
    edmontz
    @edmontz
    Int[Sin[Sin[a*x]],x] appears to be beyond any CAS I've encountered thus far. Is this type of function beyond integration. Maybe related to a
    Bessel function.
    Nasser M. Abbasi
    @nasser1
    AAA.png

    You can't get closed form antiderivative. You could find approximate series solution.

       (a x^2)/2 - (a^3 x^4)/12 + (a^5 x^6)/60 - (a^7 x^8)/315 + (
       13 a^9 x^10)/25200 - (47 a^11 x^12)/598752 + (
      15481 a^13 x^14)/1362160800 - (3947 a^15 x^16)/2554051500 + (
      451939 a^17 x^18)/2273570208000 - (
      23252857 a^19 x^20)/950352346944000 + (
      186846623 a^21 x^22)/64568056512960000 - (
      831520891 a^23 x^24)/2524611009656736000 + (
      1108990801 a^25 x^26)/30644204599008000000 - (
      143356511198507 a^27 x^28)/37217815504359602112000000 + (
      920716137922619 a^29 x^30)/2312821392056632416960000000 + 
      C[1]

    Here is a plot comparing the derivative of the above antiderivative above with the integrand showing good agreement. More terms gives better agreemeent.

       ode = y'[x] == Sin[Sin[a*x]];
       antiderivative = AsymptoticDSolveValue[ode, y[x], {x, 0, 30}]
       Plot[Evaluate[{Sin[Sin[a*x]], D[antiderivative, x]} /. a -> 1], {x, -3, 3}]
    edmontz
    @edmontz
    I tried something different, I attempted an adaptive method to find the principle components from a sample that I applied an fft to. Initially just two peaks appeared to be relevant, more iterations showed otherwise.
    So time to investigate your approach.
    edmontz
    @edmontz
    I did manage to run all of the RUBI test suites, this took about a day; I did wonder if this might be sped up with a GPU. It required about a days worth of CPU time, I just let run in the background while I continued with all of the usual computer related tasks.
    edmontz
    @edmontz
    Then, with the RUBI package loaded I attempted to solve some demanding nonlinear, second order differential equations; thinking that with RUBI the process is much more proficient . This didn't appear to be the instance. Perhaps RUBI isn't completely incorporated into Mathematica calculus routines yet.
    edmontz
    @edmontz
    Okay, I just tried your method, for a particular domain this gives the appearance of a good fit; outside of that it becomes asymptotically inaccurate. The formula for a geometric sequence, as found in math tables, sometimes returns a closed form representation.
    Albert D. Rich
    @AlbertRich

    The following Issue was recently posted on the Rubi's GitHub repository:

    • With the last public update to this repo being over a year ago, it would be great to hear if this is still actively being worked on ­čÖé.

    I posted the following response:

    • Yes, Rubi 4 is currently undergoing a major redesign that will significantly expand the class of mathematical expressions it can integrate, produce simpler antiderivatives, and provide more elegant derivations. Also it is necessary to perfect Rubi 4 before compiling its pattern matching rules into an if-then-else decision tree for the next release of Rubi.

    • I'm working fulltime on what has turned out to be a massive project. It's driven by my figuring out the math required to integrate expressions symbolically. I will release a new version of Rubi 4 as-soon-as it's perfected to my satisfaction. But it's impossible to predict when that will be, given the creative nature of this open-ended work.

    Albert

    Miguel Raz Guzmán Macedo
    @miguelraz
    Hello @AlbertRich - how goes the Rubi revamp?
    Wish you all the best an dlooking forward to it.
    Albert D. Rich
    @AlbertRich
    @miguelraz Hang tight. Hopefully a new release of Rubi will be available by the end of the year. Sorry I can't be more definitive. It's hard to predict where the FTOC will take me... Albert
    Miguel Raz Guzmán Macedo
    @miguelraz
    All the support for you @AlbertRich! Keep up the great work!
    toshiki
    @toshiki:matrix.org
    [m]
    Hi, just started using Rubi. When I use Integrate[], Mathematica often returns a result with a condition, for example, a>0 or something, I'm wondering if Rubi has this functionality. Thank you.
    Also, when I try to access the documentation using ?Int, my Mathematica freezes. I don't know if it's only a problem for my computer or there's a bug though...
    Albert D. Rich
    @AlbertRich
    @toshiki:matrix.org The antiderivatives produced by Rubi are valid for all real and complex values of their parameters. Therefore, there is no need place conditions on them. That's a good thing.
    Tci Gravifer Fang
    @Gravifer
    Hello guys! I have been through an academic hiatus for almost a year now, and only coming back to coding and stuff recently. I noticed that the rubi repo is not currently very active, and wonder what's the situation of the project at this point. Can somebody catch me up?
    Albert D. Rich
    @AlbertRich

    @Gravifer Thanks for your interest in Rubi. As previously posted:

    Rubi 4 is currently undergoing a major redesign that will significantly expand the class of mathematical expressions it can integrate, produce simpler antiderivatives, and provide more elegant derivations. Also it is necessary to perfect Rubi 4 before compiling its pattern matching rules into an if-then-else decision tree for the next release of Rubi.

    I'm working fulltime on what has turned out to be a massive project. It's driven by my figuring out the math required to integrate expressions symbolically. I will release a new version of Rubi 4 as-soon-as it's perfected to my satisfaction. But it's impossible to predict when that will be, given the creative nature of this open-ended work.

    Miguel Raz Guzmán Macedo
    @miguelraz
    @AlbertRich Happy Holidays!
    Wish you the best this year and thank you for all your hard work <3