-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Martin Albrecht wrote: > 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?
I have to rethink that statement, but in my applications typically the number of variables is large (>=64) while the equations of the ideal have small degree. On the other hand I actually have no idea what happens to them during a "primdecGTZ computation" ... Polynomials over Fields of Characteristic zero in the beginning. But the algorithms are formulated in the general setting. But all the applications that come to my mind are for characteristic 0. Probably this is different in Coding/Kryptotheory ? >> 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() Nice ... >> 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. Hmm, I just found out about "optional packages" :) But frobby does not build with my brand new gcc 4.3. ... -----BEGIN PGP SIGNATURE----- Version: GnuPG v2.0.9 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iEYEARECAAYFAkkZj7IACgkQrpEWPKIUt7Px2QCcDdV14hmugcMApmjI2s5woRt0 kKgAoJIufMXjsyRDUTmWmTCEd/JV/nEM =L9Ao -----END PGP SIGNATURE----- --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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 -~----------~----~----~----~------~----~------~--~---
