Decompositions of binomial ideals |
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Authors: | Thomas Kahle |
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Institution: | (1) University of Illinois at Chicago, Chicago, IL, USA;(2) The Pennsylvania State University, University Park, PA, USA; |
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Abstract: | We present Binomials, a package for the computer algebra system Macaulay 2, 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 a paper of Eisenbud and
Sturmfels, 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 their conjectures. |
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Keywords: | |
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