Hello,
sorry to not get back to you sooner, but I was rather busy with CoCoALib stuff today. On Feb 9, 1:56 am, "David Joyner" <[EMAIL PROTECTED]> wrote: > If the question is "are there applications of Grobner bases over ZZ?" > then the answer I believe is yes. George Nakos, a colleague 2 doors > down the hall > who implemented one of the first Grobner basis computaitons over ZZ > (for Mma, years and years ago) for the purpose of doing homotopy > computations. I don't remember any details but I vaguely remember > the point was that the fact that ZZ was needed (as opposed to a field) > corresponded to some grading that one needed to keep track of. If > details are needed, I could ask him for a reference. BTW, Mma was too slow > to make as much progress as he wanted and I don't remember if he ever > got Magma (while we had it) to do what he wanted. I think George might > still be interested in a very fast implementation over ZZ, since SAGE is free. > If you want me to ask, just tell me. > If he could write up some of his experience I certainly wouldn't mind :) We would obviously be interested if somebody would like to implement this on top of CoCoALib. 0.98 is going to be released under the GPL 2.0 without any restrictions by the end of February. I would be more than willing to give assistance and make sure that the code is up to coding convention so that it can be smoothly integrated into the library. I took a very superficial look at Chapter 4 in Adams/Loustaunau's "An Introduction To Gröbner Bases": Gröbner Bases over Rings and the main paper they refer to is by Michael Möller written in 1988. It is not available from his website at http://www.mathematik.uni-dortmund.de/lsviii/moeller/veroeffentl.html but since he sits four floors down from my office I will try to drop by on Monday and ask him if he can put it up. At least some of the algorithms from Möller's paper have been implemented in Singular (no surprise there I guess), so if there is anybody out there familiar with the Singular code base I would be thankful for pointers. My most detailed knowledge of the sources is more in the area of slimgb and the omalloc slab allocator they use, so that would save me at least some time. William also referred to "Dynamical Systems of Algebraic Origin". by Klaus Schmidt in Vienna, but I would also be interested in other articles. My time is booked up till the end of March, but this sounds like an interesting thing to do in the summer :) - if nobody else likes to do it. Cheers, Michael --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
