| Title: | On Groebner bases and their use in solving some practical problems |
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| Authors: | ID Mencinger, Matej (Author) |
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| Files: |  http://www.hrpub.org/download/201306/ujcmj.2013.010102.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
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| Abstract: | Groebner basis are an important theoretical building block of modern (polynomial) ring theory. The origin of Groebner basis theory goes back to solving some theoretical problems concerning the ideals in polynomial rings, as well as solving polynomial systems of equations. In this article four practical applications of Groebner basis theory are considered; we use Groebner basis to solve the systems of nonlinear polynomial equations, to solve an integer programming problem, to solve the problem of chromatic number of a graph, and finally we consider an original example from the theory of systems of ordinary (polynomial) differential equations. For practical computations we use systems MATHEMATICA and SINGULAR . |
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| Keywords: | polynomial system of (differential) equations, integer linear programming, chromatic number of a graph, polynomial rings, Groebner basis, CAS systems |
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| Year of publishing: | 2013 |
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| Number of pages: | str. 5-14 |
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| Numbering: | Vol. 1, no. 1 |
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| PID: | 20.500.12556/DKUM-50457  |
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| UDC: | 517.1 |
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| COBISS.SI-ID: | 17085206 |
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| NUK URN: | URN:SI:UM:DK:IBYNFQVE |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1916 |
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| Downloads: | 127 |
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| Metadata: |    |
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| Categories: | Misc.
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