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##### 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. 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. 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

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 🙂.

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