Vol. 4, No. 1, 2012

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Decompositions of binomial ideals

Thomas Kahle

Vol. 4 (2012), 1–5

The Macaulay2 package Binomials contains implementations of specialized algorithms for binomial ideals, including primary decomposition into binomial ideals. The current implementation works in characteristic zero. Primary decomposition is restricted to binomial ideals with trivial coefficients to avoid computations over the algebraic numbers. The basic ideas of the algorithms go back to Eisenbud and Sturmfels’ seminal paper on the subject. Two recent improvements of the algorithms are discussed and examples are presented.

Mathematical Subject Classification 2010
Primary: 13P15
Secondary: 13C99
Supplementary material

Binomials source code

Received: 28 June 2011
Revised: 22 September 2011
Accepted: 6 February 2012
Thomas Kahle
Forschungsinstitut für Mathematik
ETH Zürich
Office HG G 38.1
Rämistrasse 101
CH-8092 Zürich