Real algebraic and semi-algebraic sets:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Hermann, Ed. des Sciences et des Arts
1990
|
| Schriftenreihe: | Actualités mathématiques
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 340 S. graph. Darst. |
| ISBN: | 2705661441 |
Internformat
MARC
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| 100 | 1 | |a Benedetti, Riccardo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Real algebraic and semi-algebraic sets |c Riccardo Benedetti & Jean-Jacques Risler |
| 264 | 1 | |a Paris |b Hermann, Ed. des Sciences et des Arts |c 1990 | |
| 300 | |a 340 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Actualités mathématiques | |
| 650 | 7 | |a Corps ordonnés |2 ram | |
| 650 | 4 | |a Ensembles semi-algébriques | |
| 650 | 4 | |a Géométrie algébrique | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Ordered fields | |
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| 650 | 0 | 7 | |a Semialgebraische Menge |0 (DE-588)4382209-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-002957363 | ||
Datensatz im Suchindex
| _version_ | 1804118919258046464 |
|---|---|
| adam_text | Contents
Introduction 3
1 Elementary properties of single variable polynomials 7
Introduction 7
1.1 Number of roots of a polynomial 8
1.2 Some bounds on the roots 19
1.3 Separation of roots 23
1.4 Resultants and discriminants 26
1.5 Continuity of roots 33
1.6 Analyticity of simple roots and Thorn s lemma 39
1.7 Liouville functions 40
1.8 Thorn s lemma and Liouville extensions 45
2 Semi algebraic sets 49
Introduction 49
2.1 Definitions and first examples 50
2.2 The first main structure theorem 54
2.3 Applications of the first main structure theorem 59
2.4 The second main structure theorem 68
2.5 Applications of the second main structure theorem 75
2.6 Cell decomposition and triangulation of semi algebraic sets 82
2.7 Local triviality of semi algebraic maps 98
2.8 Applications of the local triviality theorem 107
2.9 A rough quantitative approach to the finiteness theorem 110
3 Real algebraic sets 117
Introduction 117
3.1 Basic definitions and first properties 118
3.2 Regular points 122
3.3 Complexification 132
3.4 Dimension 134
3.5 Some examples involving V,R{V),S{V), 137
3.6 Remarkable examples of real algebraic sets and regular maps 140
3.7 Blowing up: gluing via regular maps 149
3.8 Neighbourhoods of algebraic sets 161
3.9 (Milnor Thom) Bounds for the topology of algebraic sets 170
3.10 Local topological properties of real algebraic sets 175
4 Complexity 183
Introduction 183
4.1 Hovansky s theorem 184
4.2 Additive complexity of polynomials 194
4.3 Additive complexity of polynomials in several variables 200
4.4 Estimation of the number of connected components of a semi agebraic set . . . 206
4.5 Complexities 211
4.6 Some complements 214
5 Curves and surfaces in the projective space 231
Introduction 231
5.1 Topology of the real projective space 232
5.2 The topology of complex curves 238
5.3 Plane curves: maximal curves 245
5.4 Plane curves: other properties 260
5.5 Some complements: Applications of blowing up and Brusotti s theorem .... 264
5.6 Surfaces of degree 3 in RP3 275
5.7 Further results on the topology of smooth algebraic varieties in RP 284
A Effective calculation of subresultants 291
A.I Subresultants and sub GCDS 291
A.2 Subresultants and Euclid s algorithm 296
B Bezout s theorem 299
C Smith s theory 303
D On the piano Mover s problem 307
D.I Introduction 307
D.2 The piano mover s problem 308
D.3 Germs of plane curves 311
D.4 Families of curves 317
D.5 Applications to polynomials 320
D.6 Applications to the piano mover s problem 326
Index 333
Bibliography 336
|
| any_adam_object | 1 |
| author | Benedetti, Riccardo Risler, Jean-Jacques |
| author_facet | Benedetti, Riccardo Risler, Jean-Jacques |
| author_role | aut aut |
| author_sort | Benedetti, Riccardo |
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| building | Verbundindex |
| bvnumber | BV004807489 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 140f |
| ctrlnum | (OCoLC)23015354 (DE-599)BVBBV004807489 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004807489 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:17:57Z |
| institution | BVB |
| isbn | 2705661441 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002957363 |
| oclc_num | 23015354 |
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| physical | 340 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| publisher | Hermann, Ed. des Sciences et des Arts |
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| series2 | Actualités mathématiques |
| spelling | Benedetti, Riccardo Verfasser aut Real algebraic and semi-algebraic sets Riccardo Benedetti & Jean-Jacques Risler Paris Hermann, Ed. des Sciences et des Arts 1990 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Actualités mathématiques Corps ordonnés ram Ensembles semi-algébriques Géométrie algébrique Géométrie algébrique ram Geometry, Algebraic Ordered fields Reelle algebraische Geometrie (DE-588)4192004-1 gnd rswk-swf Semialgebraische Menge (DE-588)4382209-5 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Reelle algebraische Geometrie (DE-588)4192004-1 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Semialgebraische Menge (DE-588)4382209-5 s Risler, Jean-Jacques Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957363&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benedetti, Riccardo Risler, Jean-Jacques Real algebraic and semi-algebraic sets Corps ordonnés ram Ensembles semi-algébriques Géométrie algébrique Géométrie algébrique ram Geometry, Algebraic Ordered fields Reelle algebraische Geometrie (DE-588)4192004-1 gnd Semialgebraische Menge (DE-588)4382209-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4192004-1 (DE-588)4382209-5 (DE-588)4001161-6 |
| title | Real algebraic and semi-algebraic sets |
| title_auth | Real algebraic and semi-algebraic sets |
| title_exact_search | Real algebraic and semi-algebraic sets |
| title_full | Real algebraic and semi-algebraic sets Riccardo Benedetti & Jean-Jacques Risler |
| title_fullStr | Real algebraic and semi-algebraic sets Riccardo Benedetti & Jean-Jacques Risler |
| title_full_unstemmed | Real algebraic and semi-algebraic sets Riccardo Benedetti & Jean-Jacques Risler |
| title_short | Real algebraic and semi-algebraic sets |
| title_sort | real algebraic and semi algebraic sets |
| topic | Corps ordonnés ram Ensembles semi-algébriques Géométrie algébrique Géométrie algébrique ram Geometry, Algebraic Ordered fields Reelle algebraische Geometrie (DE-588)4192004-1 gnd Semialgebraische Menge (DE-588)4382209-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Corps ordonnés Ensembles semi-algébriques Géométrie algébrique Geometry, Algebraic Ordered fields Reelle algebraische Geometrie Semialgebraische Menge Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957363&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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