I have a question regarding converting an expression tree to holonomic For instance, we have an expression expr = sin(x)*exp(x), So traversing this gives sin(x) and exp(x). Once we have the holonomic representation of sin and exp we can use our multiplication algorithm to convert the whole expression to a holonomic one. So how is one going to get the holonomic representation of sin and exp? Do we have create some kind of table to store all the holonomic representation of elementary functions or should we develop a function to find holonomic representations?
On Tuesday, March 15, 2016 at 11:58:53 PM UTC+5:30, Ondřej Čertík wrote: > > On Tue, Mar 15, 2016 at 12:14 AM, Subham Tibra <[email protected] > <javascript:>> wrote: > > Hi Ondrej, > > Regarding the conversion of holonomic to hypergeometric, approaches I > have > > in mind: > > > > If the ratio of terms can be found out directly using the recurrence > > relation then one can get the hypergeometric representation > > Getting a closed form of the recurrence and thus computing the ratio to > > convert to hypergeometric > > Guessing the function from the coefficients in series expansions > > > > Are there any more methods which I am missing? As you wrote here > > I think those are the main once, at least as far as I know. > > >> > >> "To convert a holonomic function back to a hypergeometric one is also > >> quite easy, as one can expand the holonomic function into a (formal) > series, > >> and then compute the ratio of terms and get the hypergeometric function > out > >> of it." > > > > > > Does the ratio here means the numerical value? How one can get the > > hypergeometric function from the numerical values of the ratio? > > Not the numerical value, but a symbolic value of the ratio. Once you > have the ratio, then you factor the polynomial numerator and > denominator and read off the hypergeometric coefficients. See e.g. > here for details: > > http://www.theoretical-physics.net/dev/math/hyper.html > > > On Sunday, March 13, 2016 at 12:41:41 AM UTC+5:30, Subham Tibra wrote: > >> > >> I have few questions. > >> > >> When finding a recurrence relation for the series expansion, is it > >> required just about the origin or at any arbitrary point? > > I am not sure about that. That's a good question. I would assume an > arbitrary point, but perhaps not. > > >> > >> In cases, when the ratio of terms can be found out directly by the > >> recurrence relation or we can find the closed form of the recurrence, > we can > >> convert holonomic to hypergeometric. If these are not possible, then > what > >> would be our approach to convert to hypergeometric? > > If it's not possible, then we have to use other means, perhaps some > kind of a pattern matching. A lot of functions can be written as a > linear combination of hypergeometric functions, so I would concentrate > on that. > > Ondrej > > >> > >> On Friday, March 11, 2016 at 9:48:14 PM UTC+5:30, Subham Tibra wrote: > >>> > >>> Hi, I have created a pull request regarding this. Please give your > >>> suggestions and ideas here. > >>> > >>> On Tuesday, March 8, 2016 at 10:17:24 PM UTC+5:30, Ondřej Čertík > wrote: > >>>> > >>>> Hi Tabot, > >>>> > >>>> On Tue, Mar 8, 2016 at 4:59 AM, Tabot Kevin <[email protected]> > wrote: > >>>> > Hello Ondrej, I am really interested in this projects. Please can > you > >>>> > point > >>>> > me to steps i can take to get started familiarizing myself with the > >>>> > SymPy > >>>> > environment for this project? > >>>> > >>>> The best is to try to figure out how the holonomic functions should > be > >>>> implemented, as discussed in this thread. > >>>> > >>>> Everyone --- if you are interested in this project, definitely > >>>> consider applying. We accept the best proposals, and if two or more > >>>> proposals are accepted for similar work, GSoC allows us to amend the > >>>> work, so that you work complements each other. We've done it in the > >>>> past, e.g. with regards to fast series expansion/polynomials. > >>>> > >>>> 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] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > 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/31238a9b-1830-4e47-86a6-5b5f1f44ede1%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/b0b13bfc-3fed-4de6-b6e4-2dc02b87935a%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
