Computational synthetic geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1989
|
| Schriftenreihe: | Lecture notes in mathematics
1355 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 158 - 166 |
| Beschreibung: | 168 S. Ill., graph Darst. |
| ISBN: | 3540504788 0387504788 |
Internformat
MARC
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| 245 | 1 | 0 | |a Computational synthetic geometry |c Jürgen Bokowski ; Bernd Sturmfels |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1989 | |
| 300 | |a 168 S. |b Ill., graph Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804116860103294976 |
|---|---|
| adam_text | Table of Contents
I: PRELIMINARIES 1
1.1. What is computational synthetic geometry ? 1
1.2. Invariant theory and the Grassmann Plucker relations 7
1.3. Matroids and oriented matroids 11
II: ON THE EXISTENCE OF ALGORITHMS 18
2.1. Encoding affine algebraic varieties in matroids 18
2.2. On the algorithmic Steinitz problem 23
2.3. Real realizability versus rational realizability 28
III: COMBINATORIAL AND ALGEBRAIC METHODS 32
3.1. A basis free coordinatization algorithm for a class of matroids .... 32
3.2. Applications to n3 configurations and other examples 37
3.3. Inequality reduction and coordinatization of oriented matroids .... 50
IV: ALGEBRAIC CRITERIA FOR GEOMETRIC REALIZABILITY .... 61
4.1. Preliminaries from algebraic and semialgebraic geometry 61
4.2. Final polynomials for matroids 68
4.3. Oriented matroids, the Steinitz problem and symmetric realizations 76
4.4. On the Grassmann stratification and a problem of N.White 80
V: GEOMETRIC METHODS 87
5.1. Geometric construction and topology of a class of oriented matroids 87
5.2. On neighborly polytopes with few vertices 92
5.3. A small counterexample to a conjecture of G.Ringel 96
5.4. An integral geometry approach to oriented matroids 99
VI: RECENT TOPOLOGICAL RESULTS 102
6.1. Oriented matroids without the isotopy property 103
6.2. Simplicial polytopes without the isotopy property 106
6.3. Mnev s universality theorem 112
VII: PREPROCESSING METHODS 115
7.1 Generation of oriented matroids with specific properties 115
7.2. On the solvability sequence method 119
7.3 On the finding of final polynomials by linear programming 121
7.4. Final polynomials with symmetries 125
VIII: ON THE FINDING OF POLYHEDRAL MANIFOLDS 133
8.1. Historical remarks 133
8.2. Combinatorial theories for generating manifolds 135
8.3. Manifolds with minimal number of vertices 137
IX: MATROIDS AND CHIROTOPES AS ALGEBRAIC VARIETIES ... 147
9.1. New algebraic methods for oriented matroids 148
9.2. Syzygies for chirotope polynomials 150
9.3. Applications for planar problems 155
References 158
Index 167
|
| any_adam_object | 1 |
| author | Bokowski, Jürgen 1943- Sturmfels, Bernd 1962- |
| author_GND | (DE-588)143597590 (DE-588)121330435 |
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| author_role | aut aut |
| author_sort | Bokowski, Jürgen 1943- |
| author_variant | j b jb b s bs |
| building | Verbundindex |
| bvnumber | BV002436151 |
| classification_rvk | SI 850 |
| classification_tum | MAT 525f |
| ctrlnum | (OCoLC)230995109 (DE-599)BVBBV002436151 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002436151 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:45:13Z |
| institution | BVB |
| isbn | 3540504788 0387504788 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001581155 |
| oclc_num | 230995109 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-83 |
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| physical | 168 S. Ill., graph Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bokowski, Jürgen 1943- Verfasser (DE-588)143597590 aut Computational synthetic geometry Jürgen Bokowski ; Bernd Sturmfels Berlin [u.a.] Springer 1989 168 S. Ill., graph Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1355 Literaturverz. S. 158 - 166 Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Computer (DE-588)4070083-5 gnd rswk-swf Synthetische Geometrie (DE-588)4508971-1 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Berechenbarkeit (DE-588)4138368-0 s Synthetische Geometrie (DE-588)4508971-1 s Computer (DE-588)4070083-5 s Sturmfels, Bernd 1962- Verfasser (DE-588)121330435 aut Lecture notes in mathematics 1355 (DE-604)BV000676446 1355 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001581155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bokowski, Jürgen 1943- Sturmfels, Bernd 1962- Computational synthetic geometry Lecture notes in mathematics Algorithmische Geometrie (DE-588)4130267-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Computer (DE-588)4070083-5 gnd Synthetische Geometrie (DE-588)4508971-1 gnd |
| subject_GND | (DE-588)4130267-9 (DE-588)4138368-0 (DE-588)4070083-5 (DE-588)4508971-1 |
| title | Computational synthetic geometry |
| title_auth | Computational synthetic geometry |
| title_exact_search | Computational synthetic geometry |
| title_full | Computational synthetic geometry Jürgen Bokowski ; Bernd Sturmfels |
| title_fullStr | Computational synthetic geometry Jürgen Bokowski ; Bernd Sturmfels |
| title_full_unstemmed | Computational synthetic geometry Jürgen Bokowski ; Bernd Sturmfels |
| title_short | Computational synthetic geometry |
| title_sort | computational synthetic geometry |
| topic | Algorithmische Geometrie (DE-588)4130267-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Computer (DE-588)4070083-5 gnd Synthetische Geometrie (DE-588)4508971-1 gnd |
| topic_facet | Algorithmische Geometrie Berechenbarkeit Computer Synthetische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001581155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT bokowskijurgen computationalsyntheticgeometry AT sturmfelsbernd computationalsyntheticgeometry |