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Latin American Symposium on Theoretical Informatics

LATIN 2014: LATIN 2014: Theoretical Informatics pp 648–659Cite as

A Divide and Conquer Method to Compute Binomial Ideals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

Abstract

A binomial is a polynomial with at most two terms. In this paper, we give a divide-and-conquer strategy to compute binomial ideals. This work is a generalization of the work done by the authors in [12,13] and is motivated by the fact that any algorithm to compute binomial ideals spends a significant amount of time computing Gröbner basis and that Gröbner basis computation is very sensitive to the number of variables in the ring. The divide and conquer strategy breaks the problem into subproblems in rings of lesser number of variables than the original ring. We apply the framework on five problems – radical, saturation, cellular decomposition, minimal primes of binomial ideals, and computing a generating set of a toric ideal.

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Deepanjan Kesh

  2. Indian Institute of Technology Kanpur, Kanpur, India

    Shashank K. Mehta

Authors
  1. Deepanjan Kesh
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  2. Shashank K. Mehta
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Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Kesh, D., Mehta, S.K. (2014). A Divide and Conquer Method to Compute Binomial Ideals. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_56

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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