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
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