On Mon, Feb 29, 2016 at 5:48 AM, shubham tibra <[email protected]> wrote: > I looked at both the methods for addition algorithm( using Euclidean > algorithm for computing LCLM, or making an ansatz and converting it into a > linear system and then solving). > But the Ore algebra method will also require a class representing rings and > some basic functions like getting parent ring, generators of the ring. Does > Sympy have support for rings or Do we need to create a class for rings.
Why don't you start a wiki page and put there the exact algorithm that is needed. The polynomials in SymPy work in different rings, so in this sense, it's already implemented. SymPy doesn't have the parent ring structure as Sage. I would argue that it is not needed, at least it wasn't so far. It's easy to get buried in this abstract design stuff. Rather, let's figure out the actual technical algorithm, understand it and write it down. Only then start thinking what the right abstractions are. Questions to figure out: what are the rings needed for in ore_algebra? What kinds of rings are needed? How are they used in addition of two holonomic functions? Isn't it the case that you just choose polynomials with rational coefficients and just stick to that? In fact, since the differential equation can be multiplied by any integer, we probably only need polynomials with integer coefficients to represent a holonomic function (though rational coefficients might be needed for some intermediate calculations). > Also I think we should discuss on which approach to use, as pointed out by > Aaron solving linear system with rational coefficients may require improving > Sympy's support for matrices. I think we can use our general solver for now, cannot we? There are always things to improve and get faster or more robust results, but in this holonomic functions project, the goal is to get everything up and running (perhaps not optimally) and then iteratively improve upon that. Ondrej -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CADDwiVAXbDycbgRU0uQU00TFh-_4L9rZL%3DJGu9DFb1MZX18VvQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
