Schwartz-Zippelov teorem i neke njegove primjene

Nesterović, Klara (2015) Schwartz-Zippelov teorem i neke njegove primjene. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this diploma thesis we present the result usually called the Schwartz-Zippel lemma or the Schwartz-Zippel theorem. The nature of this theorem is basically algebraic, but it has significant applications in other areas of mathematics, such as the theory of algorithms and combinatorial theory. The thesis consists of three chapters. The main theme and objective are briefly described in the introduction. The first chapter contains a short history of the theorem’s origins, various forms of the main results by different authors and some comments of basic concepts related to this topic. The statement and a proof of the Schwartz-Zippel theorem are given in the second chapter, together with the general outline of its applications. The third and final chapter consists of some applications to problems which can be reduced to polynomial identity testing, including the existence of a perfect matching in a graph and testing of the associativity property in a groupoid.

Item Type: Thesis (Diploma thesis)
Supervisor: Šiftar, Juraj
Date: 2015
Number of Pages: 29
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 23 Oct 2015 10:05
Last Modified: 23 Oct 2015 10:05
URI: http://digre.pmf.unizg.hr/id/eprint/4176

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