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Einführung in Gröbnerbasen und Anwendungen by Buhrmester, Vanessa

Einführung in Gröbnerbasen und Anwendungen

by Vanessa Buhrmester
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Book cover type: Paperback
  • ISBN13: 9783668789500
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 24
  • Original Price: USD 13.9
  • Language: German
  • Edition: 1. Auflage
  • Item Weight: 46 grams
  • BISAC Subject(s): General

Fachbuch aus dem Jahr 2016 im Fachbereich Mathematik - Algebra, FernUniversität Hagen, Sprache: Deutsch, Abstract: Diese Einführung behandelt die von Bruno Buchberger begründeten und nach seinem Doktorvater Wolfgang Gröbner benannten Gröbnerbasen samt einer Einführung in die Theorie, Programmierung des Buchberger-Algorithmus und Erläuterung von Anwendungsbeispielen. Gröbnerbasen sind Erzeugendensysteme von Idealen in mehrdimensionalen Polynomringen K[T1, ..., Tn], die besondere Eigenschaften haben. Mit deren Eigenschaften können bestimmte Probleme aus der kommutativen Algebra und der algebraischen Geometrie gelöst werden. Zwei Beispiele für solche Probleme sind das Lösen von simultanen Nullstellengebilden oder das Idealzugehörigkeitsproblem. In meiner Arbeit führe ich zunächst grundlegende Definitionen ein, erläutere die Division mit Rest von Polynomen in mehreren Veränderlichen und stelle wichtige Sätze, wie den Hilbert'schen Basissatz vor (mit Beweis). Damit können schlie lich Gröbnerbasen definiert und näher beleuchtet werden. Anschlie end nenne ich das Buchberger-Kriterium und zeige, wie man Gröbnerbasen berechnen kann: mit dem Buchberger-Algorithmus. Die Implementierung der verallgemeinerten Polynomdivision und des Algorithmus von Buchberger sowie Anwendungsbeispiele runden die Arbeit schlie lich ab.

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