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Computation of Gröbner Bases

In: Gröbner Bases

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  • Masayuki Noro

    (Kobe University, Department of Mathematics, Graduate School of Science)

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.

Suggested Citation

  • Masayuki Noro, 2013. "Computation of Gröbner Bases," Springer Books, in: Takayuki Hibi (ed.), Gröbner Bases, edition 127, chapter 0, pages 107-163, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-54574-3_3
    DOI: 10.1007/978-4-431-54574-3_3
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