Decompositions of Binomial Ideals
Abstract
We present Binomials, a package for the computer algebra system Macaulay2, which specializes well known algorithms to binomial ideals. These come up frequently in algebraic statistics and commutative algebra, and it is shown that significant speedup of computations like primary decomposition is possible. While central parts of the implemented algorithms go back to Eisenbud and Sturmfels (1996), we also discuss a new algorithm for computing the minimal primes of a binomial ideal. All decompositions make significant use of combinatorial structure found in binomial ideals, and to demonstrate the power of this approach we show how Binomials was used to compute primary decompositions of commuting birth and death ideals of Evans et al., yielding a counterexample for a conjecture therein.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.4873
 Bibcode:
 2009arXiv0906.4873K
 Keywords:

 Mathematics  Commutative Algebra;
 68W30;
 13P10;
 60J22
 EPrint:
 15 pages, Revision after referee's comments