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Binomials :: Binomials

Binomials -- a package for binomial ideals

Description

Binomials is a package for binomial ideals with a particular focus on intersection decompositions and associated primes. For instance, if the input is a unital binomial ideal (that is generated by monomials and differences of monomials) then the functionbinomialPrimaryDecompositioncomputes a primary decomposition into binomial ideals. To this end a cyclotomic field extension of the coefficient field may be necessary which is automatically constructed using the package Cyclotomic. Binomials also implements the data type partialCharacter (see [ES96]) and several convenience functions to transform binomials into exponent vectors and vice versa. Those may be useful for manual inspection of binomial ideals.There is no special datatype for binomial ideals implemented, one just uses ideals.

Literature
  • [ES96] Binomial ideals (D. Eisenbud, B.Sturmfels, 1996).
  • [DMM10] Combinatorics of binomial primary decomposition (A. Dickenstein, L. Matusevich, E.Miller, 2010)
  • [OS00] Cellular Binomial Ideals. Primary Decomposition of Binomial Ideals (I. Ojeda, R. Piedra-Sanchez, 2000)
  • [Alt00] The chain property for the associated primes of A-graded ideals (K. Altmann, 2000)
  • [KM11] Decompositions of commutative monoid congruences and binomial ideals (T. Kahle, E. Miller, 2011)

Author

Certification a gold star

Version 1.0 of this package was accepted for publication in volume 4 of the journal The Journal of Software for Algebra and Geometry: Macaulay2 on 2012-02-06, in the article Decompositions of binomial ideals. That version can be obtained from the journal or from the Macaulay2 source code repository, svn://svn.macaulay2.com/Macaulay2/trunk/M2/Macaulay2/packages/Binomials.m2, release number 14467.

Version

This documentation describes version 1.2.1 of Binomials.

Source code

The source code from which this documentation is derived is in the file Binomials.m2.

Exports