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Gröbnerjeve baze in sistemi polinomskih enačb : diplomsko deloGolob, MetkaV diplomskem delu najprej predstavimo osnovne definicije teorije kolobarjev, ki jih potrebujemo skozi celotno diplomsko delo. Nato se seznanimo tudi s pojmi kolobarjev polinomov ene in več ... spremenljivk ter noetherskimi kolobarji. Obravnavamo predvsem lastnosti, ki jih ima komutativni kolobar polinomov F[x_1‚x_2‚…,x_{n}], kjer je F polje. V preostalih poglavjih se posvetimo študiju Gröbnerjevih baz. Gre za končne množice generatorjev posameznih idealov kolobarja F[x_1‚x_2‚…,x_{n}]. Nato opišemo algoritem splošnega deljenja polinomov, kjer so polinomi iz F[x_1‚x_2‚…,x_{n}], ki ga rabimo v nadaljevanju. Nadalje povemo še nekaj o uporabnosti Gröbnerjevih baz. Med drugim dokažemo Buchbergerjev kriterij, ki igra ključno vlogo pri Buchbergerjevem algoritmu. S pomočjo omenjenega algoritma lahko poiščemo Gröbnerjevo bazo poljubnega danega ideala. Definiramo tudi pojma minimalne in reducirane Gröbnerjeve baze ter pogledamo kako iz Gröbnerjeve baze dobimo omenjeni bazi. Teorija Gröbnerjevih baz se izkaže za zelo koristno pri reševanju algebraičnih enačb, saj služi kot osnova pri reševanju sistemov enačb, kjer nastopajo nelinearni polinomi. Zato si na koncu pogledamo še eliminacijsko teorijo, ki pove kako iz nekega sistema enačb dobiti nove enačbe, ki ne vsebujejo vseh prvotnih spremenljivk.Type of material - undergraduate thesis ; adult, seriousPublication and manufacture - Maribor : [M. Golob], 2015Language - slovenianCOBISS.SI-ID - 21725192
Author
Golob, Metka
Other authors
Romanovski, Valery |
Ferčec, Brigita
Topics
Univerzitetna in visokošolska dela |
diplomska dela |
matematika |
polinomi |
ideali |
raznoterosti |
Gröbnerjeve baze |
theses |
mathematics |
polynomials |
ideals |
varieties |
Gröbner basis
Library/institution |
City | Acronym | For loan | Other holdings |
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Miklošič Library FPNM, Maribor | Maribor | PEFMB |
reading room 1 cop.
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Shelf entry
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Year | Impact factor | Edition | Category | Classification | ||||
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JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
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DRS, in which the journal is indexed
Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Golob, Metka | |
Romanovski, Valery | 20779 |
Ferčec, Brigita | 31806 |
Source: Personal bibliographies
and: SICRIS
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