Gröbner Basis and Its Applications

  • Takafumi Shibuta
Part of the Mathematics for Industry book series (MFI, volume 5)


Computer Algebra is a field of mathematics and computer science that studies algorithms for symbolic computation. A fundamental tool in computer algebra to study polynomial ideals is the theory of Geöbner basis. The notion of the Gröbner basis and the Buchberger’s algorithm for computing it was proposed by Bruno Buchberger in 1965. Gröbner bases have numerous applications in commutative algebra, algebraic geometry, combinatorics, coding theory, cryptography, theorem proving, etc. The Buchberger’s algorithm is implemented in many computer algebra systems, such as Risa/Asir, Macaulay2, Singular, CoCoa, Maple, and Mathematica. In this chapter, we will give a short introduction on Gröbner basis theory, and then we will present some applications of Gröbner bases.


Gröbner basis Toric ideal 


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityNishi-kuJapan

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