I recommend this be crossposted to sage-devel and perhaps to sage-combinat There are people who know all about formal power series in Sage...
On Tuesday, August 16, 2016 at 9:25:08 AM UTC+1, Martin R wrote: > > Hi Waldek! (and all others of course, too!) > > Am Samstag, 13. August 2016 22:08:16 UTC+2 schrieb Waldek Hebisch: > > Well, Sage uses Maxima as its default integrator. There are whole >> classes of functions that FriCAS can integrate and Maxima can not >> (the opposite happens, but is rare). Also, it is not hard >> to find examples where Maxima gives nonelemetary answer when >> elementary integral exists. FriCAS answers are irredundant: >> nonelementary parts are necessary to express the answer. > > > integration is one (and so far the only) part of sage which actually uses > FriCAS (optionally). > > >> FriCAS has solver for differential linear ODE-s of higher >> order and for systems. IIUC Sage (via Maxima) is limited to >> order 2. >> > > Great, I added an example from one of the input files. (I know nothing > hardly anything about ODE's.) > > I belive that FriCAS limit command is stronger than Maxima >> and Sympy. The difference here is probably smaller than in >> case of integrator, but still there is reason to call >> FriCAS limit. >> > > OK, I'll check! > > >> I wonder if Sage has symbolic Jordan decomposition? FriCAS >> has (under name generalizedEigenvectors). > > > I don't know what you mean here. Sage has Jordan decomposition over > algebraic numbers. > > I checked generalizedEigenvectors matrix [[1, x], [0, 1]] but this gives a > wrong result: > > (5) -> m := matrix([[1,x],[0,1]]) > > +1 x+ > (5) | | > +0 1+ > Type: > Matrix(Polynomial(Integer)) > (6) -> generalizedEigenvectors m > > +0+ +1+ > (6) [[eigval= 1,geneigvec= [| |,| |]]] > +1+ +0+ > Type: List(Record(eigval: > Union(Fraction(Polynomial(Integer)),SuchThat(Symbol,Polynomial(Integer))),geneigvec: > > List(Matrix(Fraction(Polynomial(Integer)))))) > > >> Given activity >> of combinat group Sage probably has support for formal >> power series. But I wonder how it compares to FriCAS >> support? >> > > This is another area where FriCAS is far ahead of sage, especially > concerning expansion of expressions. > > FriCAS has various noncommutative stuff. IIUC physicists >> are interested in shuffle and related algebras and computation >> in them is related to Hall bases. While we do not have >> ready shuffle algebra needed ingerdients are present in >> FriCAS. > > > I think the only way to compete with sage in the territory of algebras is > speed. In particular, the shuffle algebra is in sage and its quite easy > to add new algebras. > > >> As a little curiosity, from 2011 we have domain for ordinals. >> At ISSAC 2015 support for ordinals was prominently present >> among new things freshly added to Maple. I guess here >> FriCAS is ahead of Maple and Maple is ahead of Sage. >> >> OK, that's another area I know nothing about and which apparently sage > doesn't have. > > Thanks for your support! Besides, the interface is now mostly ready! > > Martin > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
