Decompositions of Binomial Ideals

Details Decompositions of Binomial Ideals Decompositions of Binomial Ideals

2009-06-26

arxiv.org/abs/0906.4873v3

Mathematics

Commutative Algebra

15 pages, Revision after referee's comments

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Decompositions of Binomial Ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Decompositions of Binomial Ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Decompositions of Binomial Ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-670652