Dear David and Furkan, For sure, it is related. About the theory of symmetries of ODE one can also look in V. Arnold's text books on ODE, in the books of list of references of John Starrett's paper "Solving equations by symmetry groups", there are various texts about the symmetries of PDE, for example, the book www.amazon.com/Symmetries-Conservation-Differential-Mathematical-Translations/dp/082180958X. Therefore, theoretically the area of symmetries of DE is well-developed. Another thing is to design a package for SAGE...
El sábado, 13 de junio de 2020, 8:28:54 (UTC-5), Furkan Semih Dündar escribió: > > Dear David, > > Yes it is related. > > Dear Mikhail, > > Let us check what is developed so far as a starting point. This looks like > a good initial step. > > I have been travelling since last evening. Sorry for the relatively late > reply. > > Best wishes, > Furkan. > > 13 Haz 2020 Cmt 16:21 tarihinde David Joyner <wdjo...@gmail.com > <javascript:>> şunu yazdı: > >> Is the command >> sympy.solvers.ode.infinitesimals >> (in sympy, therefore in Sage) related to what you want? >> https://docs.sympy.org/latest/modules/solvers/ode.html#infinitesimals >> >> >> On Fri, Jun 12, 2020 at 8:07 PM Mikhail Malakhaltsev <mik...@gmail.com >> <javascript:>> wrote: >> >>> Dear Furcan, >>> >>> The topic is very interesting, there are several implementations of >>> "symmetry analysis of differential equations" in software, for example, see >>> Gerd Baumann "Symmetry Analysis of Differential Equations with >>> Mathematica", or the project jets.math.slu.cz (I did not know about the >>> book by Hans Stephani, thank you). Of course, it would be interesting to do >>> similar things in SAGE, and I could also contribute a bit to this project >>> :) >>> >>> Best wishes, >>> Mikhail >>> >>> El jueves, 11 de junio de 2020, 5:23:10 (UTC-5), Furkan Semih Dündar >>> escribió: >>>> >>>> Dearl All, >>>> >>>> I recently bought the book that I studied in my PhD years. It is >>>> "*Differential >>>> Equations: their solution using symmetries*" by Hans Stephani. >>>> https://www.amazon.com/Differential-Equations-Their-Solution-Symmetries/dp/0521355311/ref=sr_1_1?dchild=1&keywords=hans+stephani+differential+equation&qid=1591870417&sr=8-1 >>>> >>>> In the book, methods to solve nonlinear ODE's or PDE's are given if the >>>> differential equation has an underlying Lie group symmetry. I remember >>>> using the program "Reduce" in the course. It may be useful. >>>> >>>> My aim is to incorporate the methods given in the book to Sage Math. So >>>> if you are interested maybe we can form a small group to contribute to >>>> Sage >>>> in this respect. I believe the ability to solve complex differential >>>> equations is quite important for a symbolic math software. Please let me >>>> know if you are interested. >>>> >>>> Best regards, >>>> >>>> >>>> -- >>>> F. Semih Dündar >>>> >>>> -- >>> You received this message because you are subscribed to the Google >>> Groups "sage-devel" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to sage-...@googlegroups.com <javascript:>. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sage-devel/d390c411-edba-4374-b1bd-99fd14d9a255o%40googlegroups.com >>> >>> <https://groups.google.com/d/msgid/sage-devel/d390c411-edba-4374-b1bd-99fd14d9a255o%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-devel" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-...@googlegroups.com <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-devel/CAEQuuAU_2X5pG%3DAX5%3DtLscV7se%2Bmwn2MxuT77R_Vuijw%3DCwdUA%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/sage-devel/CAEQuuAU_2X5pG%3DAX5%3DtLscV7se%2Bmwn2MxuT77R_Vuijw%3DCwdUA%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/9ca06623-80c6-486d-9107-68c8cc26e8dbo%40googlegroups.com.
