If I understood your code correctly, "evaluation" is a Python function
that returns s_i, s_{i+1}, ..., s_{j} from the previous terms s_k,
..., s_{i-1}. It would be better to allow this formula to be
represented as a SymPy expression. You'll need another parameter to
specify the variables. This can easily be turned back into a function
using Lambda, but going from Python function to SymPy expression isn't
always possible.Aaron Meurer On Mon, Aug 27, 2018 at 4:38 PM, Robert Dougherty-Bliss <[email protected]> wrote: > Can you explain what you mean by symbolically? I know that there are various > classes for operations on sequences in series.sequences, but I feel like you > mean something else. (I'm not very familiar with SymPy internals other than > the "architecture" section of the contributor's guide.) > > On Monday, August 27, 2018 at 5:27:23 PM UTC-4, Aaron Meurer wrote: >> >> That looks like a good start. I would try to represent the sequence >> symbolically instead of via a function so that it can be manipulated. >> >> Aaron Meurer >> >> On Mon, Aug 27, 2018 at 2:48 PM, Robert Dougherty-Bliss >> <[email protected]> wrote: >> > The new recurrences submodule isn't quite what I had in mind. If I'm >> > reading >> > it right, it expands a C-finite recurrence into a linear combination of >> > the >> > initial values. This is good, but not a fully-fledged class. (I would >> > like >> > for this and related features to be a method of such a class.) >> > >> > My proof of concept of this idea looks like this: >> > https://gist.github.com/rwbogl/06dab1e3b9935b292354b240e1807e75 >> > >> > I'm not sure that SeqBase itself could be modified for recursive >> > sequences >> > without losing generality. >> > >> > On Monday, August 27, 2018 at 2:50:50 PM UTC-4, Aaron Meurer wrote: >> >> >> >> There has been some work on recurrences, if you search the issue >> >> tracker and pull request list for "recurrence" you can find some of >> >> it. I'm not aware of any work along the lines of what you are >> >> suggesting. >> >> >> >> Regarding the evaluation of recurrences, there has been some work in >> >> the new sympy.discrete.recurrences submodule. >> >> >> >> Making SeqBase support recursive sequences sounds like a good idea. >> >> One would need to make sure that all the methods work properly when >> >> the sequence is recursive. >> >> >> >> Aaron Meurer >> >> >> >> On Sun, Aug 26, 2018 at 1:02 PM, Robert Dougherty-Bliss >> >> <[email protected]> wrote: >> >> > I have recently been working with linear recurrence relations with >> >> > constant >> >> > and / or polynomial coefficients w.r.t. the index. (These are called >> >> > C-finite and P-recursive sequences, respectively.) These sequences >> >> > have >> >> > some >> >> > nice properties, such as easy closed-form expressions in the C-finite >> >> > case >> >> > from Binet's formula. Ultimately, I would like to do things in the >> >> > vein >> >> > of >> >> > Doron Zeilberger's GuessHolo package for P-recursive sequences, as >> >> > described >> >> > in this paper. >> >> > >> >> > Has anyone looked into creating a subclass of SeqBase (or something >> >> > more >> >> > appropriate) for recursive sequences? Perhaps specifically for >> >> > C-finite >> >> > and >> >> > P-recursive sequences? It seems like this would be convenient in >> >> > general. >> >> > For instance, every sequence implements a method to guess a C-finite >> >> > sequence that it might be (find_linear_recurrence()), but then just >> >> > returns >> >> > a list of coefficients rather than a complete sequence object. >> >> > Outside >> >> > of >> >> > C-finite sequences, memoization could be baked in to make the >> >> > evaluation >> >> > of >> >> > less-trivial recursive sequences nicer. >> >> > >> >> > -- >> >> > 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/d8c5f383-ee72-4c9a-b9a9-4c18fb91f8dd%40googlegroups.com. >> >> > For more options, visit https://groups.google.com/d/optout. >> > >> > -- >> > 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/9f96e0fc-e82a-4a28-b45a-a06cb462ac92%40googlegroups.com. >> > >> > For more options, visit https://groups.google.com/d/optout. > > -- > 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/981fcc48-bc17-403c-91b5-bce094dd3f33%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- 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/CAKgW%3D6JyJYWXKUgjRM%2Bxo15m69qXdFtoGk61ftJHrkopJ-eJ-g%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
