Hi Nijso, Thanks for linking the report! I'll check it out. I figured out the errors in the code. For now, it seems to be working on some examples given in Fritz's book and Kovacic's paper. The code is here - Rational Riccati Solver <https://gist.github.com/naveensaigit/e659941b83b52e6b78395f9bd8cbd723>. Let me know what you think of it. I'll test some of the other ODEs meanwhile.
> Also, try splitting the solver into a number of independent functions, like a function to determine poles, checking if a pole is really a pole, etc. Sure, I'll do that. Naveen On Sunday, March 28, 2021 at 8:55:52 PM UTC+5:30 nijso.be...@gmail.com wrote: > Hi Naveen, have a look at this report from the RISC group,where they list > the algebraic solutions of the kamke ODEs. Check if there are cases that > fall under case 1, or you can construct a solution yourself. Take the > solution y(x) that belongs to case 1, select a couple of poles construct a > solution and write it as a Riccati ode. > > > https://www3.risc.jku.at/publications/download/risc_5197/RISCReport15-19.pdf > > Also, try splitting the solver into a number of independent functions, > like a function to determine poles, checking if a pole is really a pole, > etc. > > Best, > Nijso > > > > > On Saturday, 27 March 2021 at 15:16:26 UTC+1 naveensai...@gmail.com wrote: > >> Hi Nijso, >> >> Are there any examples which walk through the entire algorithm? If so, >> could you please link them here? I've written a pretty basic function which >> should work for Case 1, but it doesn't. I could include the code for it too >> if required. >> >> Naveen >> On Thursday, March 25, 2021 at 10:36:37 AM UTC+5:30 Naveen Saisreenivas >> Thota wrote: >> >>> I checked some examples of laurent series expansion and the series >>> function seems to give correct results. Some examples I tested where from - >>> >>> 1. http://courses.washington.edu/ph227814/228/W14/notes/Laurent.nb.pdf >>> 2. >>> https://piazza.com/class_profile/get_resource/iw9kxycftxk6su/iy5oz4r144i6rr >>> 3. >>> https://www.maplesoft.com/support/help/Maple/view.aspx?path=numapprox/laurent >>> >>> Naveen >>> On Thursday, March 25, 2021 at 9:27:47 AM UTC+5:30 Naveen Saisreenivas >>> Thota wrote: >>> >>>> > Is the Laurent series actually needed? >>>> >>>> > I haven't read the paper but I looked at algorithm 11. Step 5 says >>>> > "compute the poles of a(x) and their orders". Is it not just asking >>>> > for the partial fraction expansion? >>>> >>>> I think Laurent Series is required in step 6 where we have to calculate >>>> the coefficient vectors for each singular point. >>>> >>>> Naveen >>>> On Wednesday, March 24, 2021 at 9:47:42 PM UTC+5:30 Oscar wrote: >>>> >>>>> On Tue, 23 Mar 2021 at 12:45, Naveen Saisreenivas Thota >>>>> <naveensai...@gmail.com> wrote: >>>>> > >>>>> > I have some doubts regarding Algorithm 11. Please help me understand >>>>> them - >>>>> ... >>>>> > >>>>> > Lastly, finding the coefficient vectors requires Laurent Series >>>>> expansion. I'm not sure if the series module can achieve this. There >>>>> seems >>>>> to be a function laurent_series, but I couldn't understand the >>>>> documentation. Perhaps Oscar could help us out here. >>>>> >>>>> Is the Laurent series actually needed? >>>>> >>>>> I haven't read the paper but I looked at algorithm 11. Step 5 says >>>>> "compute the poles of a(x) and their orders". Is it not just asking >>>>> for the partial fraction expansion? >>>>> >>>>> Oscar >>>>> >>>> -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/a782d78a-a23a-4550-be91-02e78c376bd9n%40googlegroups.com.
