On Tuesday 11 November 2008, Thomas Kahle wrote: > Dear all, Hi [sage-devel] and CC Carlo Traverso who might find this discussion relevant/.
> I would like to develop a program that does primary decomposition of > binomial ideals really fast. > Some hopefully useful algorithms are given in a '96 Paper by David > Eisenbud and Bernd Sturmfels. At least the second author is very > interested in this project and has many possible applications. > To make it fast one probably has to bring together existing software, > such as 4ti2 (www.4ti2.de), singular and new things. I think sage might > be a good platform, so here are some questions: > > Assume I wanted to derive a class binomialIdeal from e.g. > Mpolynomial_Ideal which uses specialized algorithms whenever possible > and falls back to singular if nothing special is available. > What are the things I should consider to make it fast and work well with > sage? Just to document this: We had a discussion about this off list and I raised the concern that the exponent limit of Singular (2^16-1) might become an issue. Thomas, doesn't think this will be relevant. If this is not an issue, then inheriting from the _libsingular classes might be the way to go. What base fields (rings?) are you interested in? > Who else might be interested, or has already done something in > this direction ? > > 4ti2 Integration: I know from the authors, that 4ti2 will become a C++ > Library soon. It is really fast for specific computations (e.g. > saturation of lattice ideals aka "markov basis computation"). So > probably it would be useful to have this library included in sage too. > > Integer Lattices are all over the place with binomial ideals. Are there > classes for integer lattices, or is someone working on such things? We have some lattice algorithms (LLL and BKZ) which act on integer matrices: sage: A = random_matrix(ZZ, 10, 10) sage: A.LLL() sage: A.BKZ() > Is there a class for monomial ideals already ? There are some > specialized algorithms for that which definitely should be used. There was some discussion on Frobby by Bjarke Roune. It is an optional package for now. I am not sure how mature the interface is. Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
