Dear all, 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? 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? Is there a class for monomial ideals already ? There are some specialized algorithms for that which definitely should be used. Any comment is appreciated. Thank you already. Thomas Kahle --------------------------------------------------------------------- Thomas Kahle Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26, 04103 Leipzig Tel: +49(0) 341-9959-545 [EMAIL PROTECTED], http://personal-homepages.mis.mpg.de/kahle/ ---------------------------------------------------------------------
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