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Published in:
2014 | OriginalPaper | Chapter
Gröbner Basis and Its Applications
Author : Takafumi Shibuta
Published in: A Mathematical Approach to Research Problems of Science and Technology
Publisher: Springer Japan
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Abstract
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.