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 <http://sites.math.rutgers.edu/~zeilberg/tokhniot/GuessHolo2> package for P-recursive sequences, as described in this paper <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.441.2487&rep=rep1&type=pdf> .
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.
