An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
[2020]
|
| Series: | Memoirs of the American Mathematical Society
volume 263, number 1277 (seventh of 7 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 123-125 |
| Physical Description: | v, 125 Seiten Illustrationen |
| ISBN: | 9781470441081 |
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| adam_text | American Mathematical Society
Number 1277
An Elementary Recursive Bound for
Effective Positivstellensatz and
Hilbert’s 17th Problem
Henri Lombardi
Daniel Perrucci
Marie-Frangoise Roy
ULB Darmstadt
20396563
Universitäts- und
Landesbibliothek
Darmstadt
January 2020 • Volume 263 • Number 1277 (seventh of 7 numbers)
, v tin American
•v A /i n Mathematical
SOCIETY
Contents
Chapter 1 Introduction 1
1 1 Hilbert’s 17th problem 1
1 2 Positivstellensatz 1
1 3 Historical background on constructive proofs and degree bounds 4
1 4 Our results 5
1 5 Organization of the paper 8
Acknowledgements 8
Chapter 2 Weak inference and weak existence 9
2 1 Weak inference 9
2 2 Weak existence 18
2 3 Complex numbers 21
2 4 Identical polynomials 25
2 5 Matrices 27
Chapter 3 Intermediate value theorem 29
3 1 Intermediate value theorem 29
3 2 Real root of a polynomial of odd degree 32
Chapter 4 Fundamental theorem of algebra 35
4 1 Fundamental theorem of algebra 35
4 2 Decomposition of a polynomial into irreducible real factors 41
4 3 Decomposition of a polynomial into irreducible
real factors with multiplicities 46
Chapter 5 Hermite’s Theory 53
5 1 Signature of Hermite’s quadratic form and real root counting 53
5 2 Signature of Hermite’s quadratic form and signs
of principal minors 59
5 3 Sylvester Inertia Law 73
5 4 Hermite’s quadratic form and Sylvester Inertia Law 77
Chapter 6 Elimination of one variable 81
6 1 Thom encoding of real algebraic numbers 82
6 2 Conditions on the parameters fixing the Thom encoding 86
6 3 Conditions on the parameters fixing the real root order on a family 98
6 4 Realizable sign conditions on a family of polynomials 104
iii
CONTENTS
iv
Chapter 7 Proof of the main theorems 113
Chapter 8 Annex 119
|
| adam_txt |
American Mathematical Society
Number 1277
An Elementary Recursive Bound for
Effective Positivstellensatz and
Hilbert’s 17th Problem
Henri Lombardi
Daniel Perrucci
Marie-Frangoise Roy
ULB Darmstadt
20396563
Universitäts- und
Landesbibliothek
Darmstadt
January 2020 • Volume 263 • Number 1277 (seventh of 7 numbers)
, v\ tin American
•v A \/i n Mathematical
SOCIETY
Contents
Chapter 1 Introduction 1
1 1 Hilbert’s 17th problem 1
1 2 Positivstellensatz 1
1 3 Historical background on constructive proofs and degree bounds 4
1 4 Our results 5
1 5 Organization of the paper 8
Acknowledgements 8
Chapter 2 Weak inference and weak existence 9
2 1 Weak inference 9
2 2 Weak existence 18
2 3 Complex numbers 21
2 4 Identical polynomials 25
2 5 Matrices 27
Chapter 3 Intermediate value theorem 29
3 1 Intermediate value theorem 29
3 2 Real root of a polynomial of odd degree 32
Chapter 4 Fundamental theorem of algebra 35
4 1 Fundamental theorem of algebra 35
4 2 Decomposition of a polynomial into irreducible real factors 41
4 3 Decomposition of a polynomial into irreducible
real factors with multiplicities 46
Chapter 5 Hermite’s Theory 53
5 1 Signature of Hermite’s quadratic form and real root counting 53
5 2 Signature of Hermite’s quadratic form and signs
of principal minors 59
5 3 Sylvester Inertia Law 73
5 4 Hermite’s quadratic form and Sylvester Inertia Law 77
Chapter 6 Elimination of one variable 81
6 1 Thom encoding of real algebraic numbers 82
6 2 Conditions on the parameters fixing the Thom encoding 86
6 3 Conditions on the parameters fixing the real root order on a family 98
6 4 Realizable sign conditions on a family of polynomials 104
iii
CONTENTS
iv
Chapter 7 Proof of the main theorems 113
Chapter 8 Annex 119 |
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| isbn | 9781470441081 |
| language | English |
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| physical | v, 125 Seiten Illustrationen |
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| publisher | American Mathematical Society |
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| spelling | Lombardi, Henri (DE-588)1208939033 aut An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy seventeenth Providence, RI American Mathematical Society [2020] v, 125 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 263, number 1277 (seventh of 7 numbers) Literaturverzeichnis: Seite 123-125 Hilbertsches Problem 17 (DE-588)1209288494 gnd rswk-swf Hilbertsches Problem 17 (DE-588)1209288494 s DE-604 Perrucci, Daniel (DE-588)1208939254 aut Roy, Marie-Françoise 1950- (DE-588)120268221 aut Memoirs of the American Mathematical Society volume 263, number 1277 (seventh of 7 numbers) (DE-604)BV008000141 1277 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lombardi, Henri Perrucci, Daniel Roy, Marie-Françoise 1950- An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem Memoirs of the American Mathematical Society Hilbertsches Problem 17 (DE-588)1209288494 gnd |
| subject_GND | (DE-588)1209288494 |
| title | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem |
| title_alt | seventeenth |
| title_auth | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem |
| title_exact_search | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem |
| title_exact_search_txtP | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem |
| title_full | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy |
| title_fullStr | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy |
| title_full_unstemmed | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy |
| title_short | An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem |
| title_sort | an elementary recursive bound for effective positivstellensatz and hilbert s 17th problem |
| topic | Hilbertsches Problem 17 (DE-588)1209288494 gnd |
| topic_facet | Hilbertsches Problem 17 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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