Sorry for catching up so late, The Maple package for differential algebra, mostly written by François Boulier, has been ported to SAGE. It is not part of SAGE yet, but we hope that it will soon be.
In any case, you can follow its progress there : http://trac.sagemath.org/sage_trac/ticket/13268 If you're feeling adventurous, you can apply the patches to your own SAGE installation, rebuild, and enjoy :) -- Charles Bouillaguet Le jeudi 30 juillet 2009 09:05:32 UTC+2, Martin Rubey a écrit : > William asked me to forward his reply... > > (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/ -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
