On Tuesday, 24 March 2015 22:25:04 UTC+5:30, Aaron Meurer wrote: > > I think you guys are perhaps talking past each other. To Ondrej, > "series" means "series approximation", whereas to "Sartaj" it menas > "formal power series". Both are mathematically related, but from a CAS > point of view they are quite different. > Oh, I see. I am inclined towards infinite representation of Formal Power Series. But it is easy to represent it in truncated form.
> Formal power series is something that would be nice for SymPy to have, > but my understanding is that the summation algorithms will need to > improve a lot for you to be able to compute anything nontrivial (like > Cauchy products). > Yes, you are correct summation algorithm need to be improved, some formulas are quite involved. But it will be nice to use ring_series for various operations for truncated series. When summations algorithm improve, non-trivial cases can be implemented for infinite series. Sartaj Singh Aaron Meurer > > On Mon, Mar 23, 2015 at 7:12 PM, Ondřej Čertík <[email protected] > <javascript:>> wrote: > > On Mon, Mar 23, 2015 at 1:41 AM, Sartaj Singh <[email protected] > <javascript:>> wrote: > >> It looks like ring_series, works only for finite cases, can it be > extended > >> for infinite case? SeriesData will just zip two sequences together. It > is > >> more general as variables can even be of the form sin(n*x), and not > only x. > >> In the main FormalPowerSeries class, I plan to provide an infinite > >> representation of series. > > > > I think the ring series can only be used for n terms, i.e. if you have > > some expression, like sin(x)*cos(x), then you first expand sin(x) and > > cos(x) into n-terms, and then you multiply them out, and cut the > > result appropriately (at n-terms in this case). > > > > But you can use any "n". How do you store infinite number of terms in > > your approach? > > > >> Ring_series is undoubtedly fast, so it is a plus to use it in my > >> implementation. I have glanced over the code of ring_series, and it may > be > >> modeled into the structure I propose, i.e based on sequences. The > algorithms > >> in ring_series can be used for manipulating truncated form of the > series. > >> > >> In summary, I think SeriesData should be left as a higher abstraction, > and > >> operations for truncated series can be added in SeriesX or in > >> FormalPowerSeries. Let me know what you think. > > > > That would work. > > > > 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 http://groups.google.com/group/sympy. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CADDwiVBTqTBBFCUUu_pgXNyvAibPU2ObX3_JMVQac8YAk1MtiQ%40mail.gmail.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 http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/0fadbdc4-41ea-4735-a9f5-83e18395d746%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
