Computation of Gröbner Bases

Masayuki Noro ()
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Masayuki Noro: Kobe University, Department of Mathematics, Graduate School of Science

Chapter Chapter 3 in Gröbner Bases, 2013, pp 107-163 from Springer

Abstract: Abstract In Chap. 1, we presented the theoretical foundation of Gröbner bases, and many of our computations were carried out by hand. When we want to apply Gröbner bases to practical problems, however, in most cases, we will need the help of computers. There are many mathematical software systems which support the computation of Gröbner bases, but we will often encounter cases which require careful settings or preprocessing in order to be efficient. In this chapter, we explain various methods to efficiently use a computer to compute Gröbner bases. We also present some algorithms for performing operations on the ideals realized by Gröbner bases. These operations are implemented in several mathematical software systems: Singular, Macaulay2, CoCoA, and Risa/Asir. We will illustrate the usage of these systems mainly by example.

Keywords: Polynomial Ring; Hilbert Function; Primary Decomposition; Base Ring; Initial Monomial (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-54574-3_3

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DOI: 10.1007/978-4-431-54574-3_3

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