Frobby is currently an optional component of Sage, which performs computations related to monomial ideals. In particular, it can compute
* Multigraded Hilbert series * Alexander dual of monomial ideals * Maximal standard monomials of monomial ideals * Irreducible decomposition of monomial ideals * Optimization of any linear function over the maximal standard monomials of a monomial ideal using branch-and-bound. Sage currently is not able to do any of this. Sage does have the less general (1,..., 1)-graded Hilbert series using Singular, but it doesn't support arbitrarily large exponents as Frobby does. Applications of the last item above include Frobenius numbers for instances with very large numbers (with 4ti2), as demonstrated at Sage Days 16, and described in (1) below. Another application is the integer programming gap (also with 4ti2) of a matrix where the right- hand-side is allowed to vary as described in (2). This is put up for a vote now since I wrote a cython interface to Frobby at Sage Day 16, and I'm told this requires Frobby to be a standard component of Sage. Frobby is fastest at items 2-4 listed above as documented in (3) below, by factors of up to 1000x, with the exception of specially- constructed inputs (in particular taking the dual of a dual to recover the original ideal). Item 1 is Hilbert series, where CoCoALib might be faster right now, since the algorithm I use is for now unpublished, and I haven't compared it to CoCoALib yet. In any case I will also implement the Bigatt et.al. algorithm that CoCoALib uses, though this is not done yet. Frobby has an extensive test-suite, which includes running Frobby under valgrind to detect memory leaks, and is supported for Mac OS 10.5, Linux and Cygwin. It compiles using MS Visual Studio Express, though I haven't tested it on that platform since I couldn't get GMP to build on Windows. GMP is the only dependency Frobby has other than a C++ compiler. The build system is make-based. I am the upstream contact, and Frobby is licensed as GPL version 2.0 or later. Cheers Bjarke Hammersholt Roune www.broune.com (1) Bjarke H. Roune, Solving Thousand Digit Frobenius Problems Using Grobner Bases Journal of Symbolic Computation (January 2008), volume 43, issue 1 See http://www.broune.com/papers/index.html (2) Hocsten, S., Sturmfels, B., 2007. Computing the integer programming gap. Combinatorica 27 (3). See http://arxiv.org/abs/arXiv:math/0301266 (3) Bjarke H. Roune, The Slice Algorithm For Irreducible Decomposition of Monomial Ideals Journal of Symbolic Computation (April 2009), volume 44, issue 4 See http://www.broune.com/papers/index.html --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
