On the Applications of Grobner Basis

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Parviz, Maghsoud | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41618 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Pournaki, Mohammad Reza
Abstract:
Grobner bases were introduced by Bruno Buchberger in 1965. The terminology acknowledges the influence of Wolfgang Grobner on Buchberger’s work. He introduced a specific generator for ideals in the ring of polynomials over a field and then gave an algorithm for computing of that generator. It leads to solutions to a large number of algorithmic problems that are related to polynomials in several variables. Most notably, algorithms that involve Grobner basis computations allow exact conclusions on the solutions of systems of nonlinear equations, such as the (geometric) dimension of the solution set,the exact number of solutions in case there are finitely many, and their actual computation with arbitrary precision
Keywords:
Algebraic Attack ; Coding ; Decoding Algorithm ; Grobner Basis ; Normal Form ; Affine Variety ; Shift Registers

No TOC