Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from con… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids.It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field.Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties.Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field.The necessary background knowledge is reviewed briefly.The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.; PDF; Scientific, Technical and Medical > Mathematics > Geometry, Springer Berlin Heidelberg<
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Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from con… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids.It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field.Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties.Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field.The necessary background knowledge is reviewed briefly.The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.; PDF; Scientific, Technical and Medical > Mathematics > Geometry, Springer Berlin Heidelberg<
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Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from co… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research., Springer<
*Computational Synthetic Geometry* / pdf eBook für 24.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissen… Mehr…
*Computational Synthetic Geometry* / pdf eBook für 24.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Mathematik, Springer Berlin Heidelberg<
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Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from con… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids.It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field.Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties.Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field.The necessary background knowledge is reviewed briefly.The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.; PDF; Scientific, Technical and Medical > Mathematics > Geometry, Springer Berlin Heidelberg<
No. 9783540460138. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from con… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces.This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids.It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field.Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties.Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field.The necessary background knowledge is reviewed briefly.The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.; PDF; Scientific, Technical and Medical > Mathematics > Geometry, Springer Berlin Heidelberg<
No. 9783540460138. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from co… Mehr…
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research., Springer<
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*Computational Synthetic Geometry* / pdf eBook für 24.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissen… Mehr…
*Computational Synthetic Geometry* / pdf eBook für 24.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Mathematik, Springer Berlin Heidelberg<
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Detailangaben zum Buch - Computational Synthetic Geometry
EAN (ISBN-13): 9783540460138 Erscheinungsjahr: 2006 Herausgeber: Springer Berlin Heidelberg
Buch in der Datenbank seit 2017-03-14T21:15:50+01:00 (Berlin) Detailseite zuletzt geändert am 2024-03-15T17:05:26+01:00 (Berlin) ISBN/EAN: 9783540460138
ISBN - alternative Schreibweisen: 978-3-540-46013-8 Alternative Schreibweisen und verwandte Suchbegriffe: Autor des Buches: bokowski, tom dieck, sturmfels Titel des Buches: computational geometry
Daten vom Verlag:
Autor/in: Jürgen Bokowski; Bernd Sturmfels Titel: Lecture Notes in Mathematics; Computational Synthetic Geometry Verlag: Springer; Springer Berlin 172 Seiten Erscheinungsjahr: 2006-11-14 Berlin; Heidelberg; DE Sprache: Englisch 24,60 € (DE) 25,30 € (AT) 36,00 CHF (CH) Available VIII, 172 p.
EA; E107; eBook; Nonbooks, PBS / Mathematik/Geometrie; Geometrie; Verstehen; Mathematica; Microsoft Access; Processing; Vector space; boundary element method; complexity; computer algebra; construction; discrete geometry; eXist; field; knowledge; manifold; mathematics; theorem; B; Geometry; Mathematics and Statistics; BC
Preliminaries.- On the existence of algorithms.- Combinatorial and algebraic methods.- Algebraic criteria for geometric realizability.- Geometric methods.- Recent topological results.- Preprocessing methods.- On the finding of polyheadral manifolds.- Matroids and chirotopes as algebraic varieties.
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