Algoritmi na polinomima

Zlodi, Ivana (2014) Algoritmi na polinomima. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this thesis, we have proved the division algorithm for polynomials in several variables with respect to a fixed monomial order. We have got this algorithm by extending the division algorithm for polynomials in one variable. It was shown that the remainder is not uniquely characterized as in the case of one variable. By introduction Groebner’s basis we have shown that the algorithm achieves full potential when it is paired with Groebner basis. Also, every nonzero ideal in a polynomial ring has Groebner base, and we learned how to check whether the base is Groebner. We showed by using a division algorithm and Groebner basis how to check if polynomial lies in the ideal. Finally, we showed how to construct Groebner base with Buchberger’s algorithm.

Item Type: Thesis (Diploma thesis)
Supervisor: Muić, Goran
Date: 2014
Number of Pages: 29
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 02 Sep 2015 11:11
Last Modified: 02 Sep 2015 11:11
URI: http://digre.pmf.unizg.hr/id/eprint/4211

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