REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21430
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorSchwarzweller, Christoph-
dc.date.accessioned2026-11-05T07:59:46Z-
dc.date.available2026-11-05T07:59:46Z-
dc.date.issued2005-
dc.identifier.citationFormalized Mathematics, Volume 13, Issue 1, Pages 147-156pl
dc.identifier.issn1426-2630-
dc.identifier.urihttp://hdl.handle.net/11320/21430-
dc.description.abstractWe continue the formalization of Groebner bases following the book “Groebner Bases– A Computational Approach to Commutative Algebra” by Becker and Weispfenning. Here we prove Buchberger’s first criterium on avoiding S-polynomials: S-polynomials for polynomials with disjoint head terms need not be considered when constructing Groebner bases. In the course of formalizing this theorem we also introduced the splitting of a polynomial in an upper and a lower polynomial containing the greater resp. smaller terms of the original polynomial with respect to a given term order.pl
dc.language.isoenpl
dc.publisherUniversity of Białystokpl
dc.rightsCC BY-SA 4.0-
dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
dc.titleConstruction of Gröbner Bases: Avoiding S-Polynomials– Buchberger’s First Criteriumpl
dc.typeArticlepl
dc.rights.holder© 2005 University of Białystokpl
dc.rights.holderThis work is licensed under the Creative Commons License.pl
dc.description.AffiliationUniversity of Gdańskpl
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.pl
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.pl
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.pl
dc.description.referencesGrzegorz Bancerek. Reduction relations. Formalized Mathematics, 5(4):469–478, 1996.pl
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.pl
dc.description.referencesGrzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485–492, 1996.pl
dc.description.referencesJózef Białas. Properties of fields. Formalized Mathematics, 1(5):807–812, 1990.pl
dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.pl
dc.description.referencesCzesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521–527, 1990.pl
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.pl
dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35–40, 1990.pl
dc.description.referencesEugeniusz Kusak, Wojciech Leo´nczuk, and Micha l Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.pl
dc.description.referencesGilbert Lee and Piotr Rudnicki. On ordering of bags. Formalized Mathematics, 10(1):39-46, 2002.pl
dc.description.referencesMichał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3–11, 1991.pl
dc.description.referencesMichał Muzalewski and Wojciech Skaba. From loops to abelian multiplicative groups with zero. Formalized Mathematics, 1(5):833–840, 1990.pl
dc.description.referencesYatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Formalized Mathematics, 5(2):167–172, 1996.pl
dc.description.referencesPiotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95–110, 2001.pl
dc.description.referencesChristoph Schwarzweller. More on multivariate polynomials: Monomials and constant polynomials. Formalized Mathematics, 9(4):849–855, 2001.pl
dc.description.referencesChristoph Schwarzweller. Characterization and existence of Gr¨obner bases. Formalized Mathematics, 11(3):293–301, 2003.pl
dc.description.referencesChristoph Schwarzweller. Construction of Gröbner bases. S-polynomials and standard representations. Formalized Mathematics, 11(3):303–312, 2003.pl
dc.description.referencesChristoph Schwarzweller. Polynomial reduction. Formalized Mathematics, 11(1):113–123, 2003.pl
dc.description.referencesChristoph Schwarzweller. Term orders. Formalized Mathematics, 11(1):105–111, 2003.pl
dc.description.referencesAndrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9–11, 1990.pl
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.pl
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.pl
dc.description.referencesWojciech A. Trybulec and Grzegorz Bancerek. Kuratowski– Zorn lemma. Formalized Mathematics, 1(2):387–393, 1990.pl
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.pl
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73–83, 1990.pl
dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.pl
dc.description.referencesEdmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85–89, 1990.pl
dc.identifier.eissn1898-9934-
dc.description.volume13pl
dc.description.issue1pl
dc.description.firstpage147pl
dc.description.lastpage156pl
dc.identifier.citation2Formalized Mathematicspl
Występuje w kolekcji(ach):Formalized Mathematics, 2005, Volume 13, Issue 1

Pliki w tej pozycji:
Plik Opis RozmiarFormat 
Construction_of_Grobner_Bases.pdf123,17 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki


Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons