Re: Differential algebra support
Daniel Bearup
Does SAGE incorporate support for differential algebra? That is can it
handle differential rings/ideals and does it have an implementation of
the Rosenfeld-Groebner and Ritt algorithms?
Thanks,
Daniel
John H Palmieri
wrote:
Implement them and submit a patch.
John
William Stein
Is this the same thing as "D-modules"? If so, Singular (which is in
Sage) has some major package(s) for this:
http://portal.acm.org/citation.cfm?id=1390768.1390794
(there may be more or something else -- I saw a talk on this recently
at MEGA but don't remember the details).
Macaulay 2 also has a package:
http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.2/share/doc/Macaulay2/Dmodules/html/
There is a Sage <--> Macaulay 2 interface.
As John Palmieri says, there's nothing "native" in Sage itself yet though.
-- William
kcrisman
modules, but not the same. Kaplansky has a book about this I've
always meant to read...
Maple definitely supports this; it was unclear whether Mma does,
though apparently not directly. I could not find any reference to
this on the Singular or Macaulay sites, though I may not have looked
hard enough.
In any case, either exposing this functionality to the typical user if
it's in Singular, finding an appropriately licensed piece to stick in,
or starting a new implementation for Sage sounds like a great idea for
someone who is so inclined and very conversant with the material :)
- kcrisman
On Jul 29, 11:21 am, William Stein <wst...@gmail.com> wrote:
> On Wed, Jul 29, 2009 at 7:56 AM, Daniel
>
>
> > Apologies if this is the wrong place to ask this question.
>
> > Does SAGE incorporate support for differential algebra? That is can it
> > handle differential rings/ideals and does it have an implementation of
> > the Rosenfeld-Groebner and Ritt algorithms?
>
> Is this the same thing as "D-modules"? If so, Singular (which is in
> Sage) has some major package(s) for this:
>
> http://portal.acm.org/citation.cfm?id=1390768.1390794
>
> (there may be more or something else -- I saw a talk on this recently
> at MEGA but don't remember the details).
>
Martin Rubey
I'm not sure, but I believe that FriCAS has this. At the very least, a
grep for "Ritt" in fricas/src/algebra yields some promising hits. I'm
not very familiar with Differential algebra, but William Sit is, I
guess...
Martin
Martin Rubey
(One remark: William always developed for Axiom. In Sage, the variant
of Axiom usually provided is FriCAS. To the best of my knowledge, all
libraries developed for Axiom is provided by FriCAS as well.)
"William Sit" <wy...@sci.ccny.cuny.edu> writes:
> Dear Martin:
>
> I just noticed that I can't post on the Sage support group. Would you
> please forward the following (revised for typos and grammar) to
> Daniel? thanks.
>
> William
>
> Dear Daniel and Martin:
>
> I have not kept up with all the newest development of software in
> differential algebra, but my impression is that Maple has the most
> abundance, particularly with regard to the Rosenfeld-Groebner
> algorithm. People most familiar with the Mape implementation are
> Elizabeth Mansfield, Evelyn Hubert, Francois Boulier, Ziming Li,
> Morena Maza, and perhaps a few more. I am not familiar at all with
> SAGE.
>
> That said, I don't believe the Ritt algorithm (if by this you mean
> the algorithm to decompose a radical differential ideal into its
> prime components) has ever been implemented, since there is no
> algorithm yet to test inclusion of prime differential ideals given by
> characteristic sets. I wonder whether even the Risch, or the Kovacic
> algorithm, has been fully implemented (emphasis on "fully"). The
> expert on these was Manuel Bronstein, who unfortunately passed away
> in 2006. I am not familar with what Bronstein has implemented, but I
> think it is mostly for linear ODE, second and third order. These are
> all related to differential Galois theory (more precisely,
> Picard-Vessiot theory). Jacque Artur-Weil would be one of the experts
> on this.
>
> As far as I know, there has been (was?) no abstract implementation of
> differential polynomial categories except in Axiom (I did that), and
> there the implementation is rudimentary; for example, there is no
> domain for differential ideals. Computationally, of course, one
> always deals with a finite set of differential polynomials and so it
> can be argued that there is no need to have an abstract
> implementation, but that was the question Daniel asked.
>
> Moreover, to implement abstractly partial differential polynomial
> rings is quite tricky. Many years ago, I had a project advising a
> student to implement that in Axiom. The student, a very bright one,
> was overwhelmed by the layers of abstraction even just to deal with
> input methods and notation, which I insisted should be very general,
> in accordance with the philosophy of Axiom. Later, the student
> quitted, my funds ran out and, alas, the commercial version of Axiom
> also died. I did not complete the project.
>
> I have implemented in Axiom the algorithm Leon Pritchard and I
> developed to handle initial value problems for general, first order,
> ODEs. I have not written up the documentation and hence the
> implementation is still private. I don't have time to do that, given
> the high standard required by Tim Daly, but the algorithms are
> straight forward, as described in our joint paper.
>
> I hope this brief reply will be helpful,
>
> William
>
> William Sit, Professor Emeritus
> Mathematics, City College of New York Office:
> R6/202C Tel: 212-650-5179
> Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/