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An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert's 17th Problem
The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials 2...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1920.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 020 | |a 9781470456627 | ||
| 020 | |a 1470456621 | ||
| 029 | 1 | |a AU@ |b 000069467547 | |
| 035 | |a (OCoLC)1151201237 | ||
| 050 | 4 | |a QA161.P59 |b .L66 2020 | |
| 082 | 0 | 4 | |a 512.9422 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Lombardi, Henri. | |
| 245 | 1 | 3 | |a An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert's 17th Problem |
| 260 | |a Providence : |b American Mathematical Society, |c 1920. | ||
| 300 | |a 1 online resource (138 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v. 263 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover -- Title page -- Chapter 1. Introduction -- 1.1. Hilbert's 17th problem -- 1.2. Positivstellensatz -- 1.3. Historical background on constructive proofs and degree bounds -- 1.4. Our results -- 1.5. Organization of the paper -- Acknowledgements -- Chapter 2. Weak inference and weak existence -- 2.1. Weak inference -- 2.2. Weak existence -- 2.3. Complex numbers -- 2.4. Identical polynomials -- 2.5. Matrices -- Chapter 3. Intermediate value theorem -- 3.1. Intermediate value theorem -- 3.2. Real root of a polynomial of odd degree -- Chapter 4. Fundamental theorem of algebra | |
| 505 | 8 | |a 4.1. Fundamental theorem of algebra -- 4.2. Decomposition of a polynomial into irreducible real factors -- 4.3. Decomposition of a polynomial into irreducible real factors with multiplicities -- Chapter 5. Hermite's Theory -- 5.1. Signature of Hermite's quadratic form and real root counting -- 5.2. Signature of Hermite's quadratic form and signs of principal minors -- 5.3. Sylvester Inertia Law -- 5.4. Hermite's quadratic form and Sylvester Inertia Law -- Chapter 6. Elimination of one variable -- 6.1. Thom encoding of real algebraic numbers | |
| 505 | 8 | |a 6.2. Conditions on the parameters fixing the Thom encoding -- 6.3. Conditions on the parameters fixing the real root order on a family -- 6.4. Realizable sign conditions on a family of polynomials -- Chapter 7. Proof of the main theorems -- Chapter 8. Annex -- Bibliography -- Back Cover | |
| 520 | |a The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials 2^{ 2^{ 2^{d^{4^{k}}} } } where d is the number of variables of the input polynomial. The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely the authors give an algebraic certificate of the emptyness of the realization of. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Polynomials. | |
| 650 | 0 | |a Algebraic fields. | |
| 650 | 0 | |a Recursive functions. | |
| 650 | 0 | |a Algebraic stacks. | |
| 650 | 6 | |a Polynômes. | |
| 650 | 6 | |a Corps algébriques. | |
| 650 | 6 | |a Fonctions récursives. | |
| 650 | 7 | |a Algebraic stacks |2 fast | |
| 650 | 7 | |a Algebraic fields |2 fast | |
| 650 | 7 | |a Polynomials |2 fast | |
| 650 | 7 | |a Recursive functions |2 fast | |
| 700 | 1 | |a Perrucci, Daniel. | |
| 700 | 1 | |a Roy, Marie-Françoise. | |
| 758 | |i has work: |a An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGQcRvqqDwF9Q77HrfjHYd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Lombardi, Henri. |t An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert's 17th Problem. |d Providence : American Mathematical Society, ©1920 |z 9781470441081 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6176749 |z Texto completo |
| 936 | |a BATCHLOAD | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6176749 | ||
| 994 | |a 92 |b IZTAP | ||