Martin R wrote:
>
> > I doubt that this is the case. Just consider why would you call FriCAS
> from sage for a computation? I can only think of two reasons:
>
> 1) the functionality is not available in sage. (quite unlikely, meanwhile,
> although there are some bits)
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.
FriCAS has solver for differential linear ODE-s of higher
order and for systems. IIUC Sage (via Maxima) is limited to
order 2.
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.
I wonder if Sage has symbolic Jordan decomposition? FriCAS
has (under name generalizedEigenvectors). Given activity
of combinat group Sage probably has support for formal
power series. But I wonder how it compares to FriCAS
support?
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.
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.
>
> 2) FriCAS is much faster. In this case, you probably won't care about a
> second lost because of a slow interface.
It depends. If you want to call routine thousends of times
per second than even if base routine is significantly faster
the effective speed may be lower due to interface overheads.
--
Waldek Hebisch
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