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020 a| 9781470441081q| (paperback);

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100 1 a| Lombardi, Henri.=| ^A1291096;

245 13 a| An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problemh| [electronic resource] /c| Henri Lombardi, Daniel Perrucci, Marie-Fran©ʹoise Roy.;

260 a| Providence, RI :b| American Mathematical Society,c| 2020.;

300 a| v, 125 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 263v| number 1277;

504 a| Includes bibliographical references.;

505 0 a| Weak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex.;

506 a| Available only to authorized users.;

520 a| "We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2℗ø(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Polynomials.=| ^A25840;

650 0 a| Algebraic fields.=| ^A295088;

650 0 a| Recursive functions.=| ^A30764;

650 7 a| Field theory and polynomials -- Real and complex fields -- Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx].2| msc;

650 7 a| Algebraic geometry -- Real algebraic and real analytic geometry -- None of the above, but in this section.2| msc;

650 7 a| Commutative algebra -- Topological rings and modules [See also 16W60, 16W80] -- Real algebra [See also 12D15, 14Pxx].2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Perrucci, Daniel.?| UNAUTHORIZED;

856 40 z| Full text available from Memoirs of the American Mathematical Societyu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.ams.org%2Fbooks%2Fmemo%2F1277;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6176749;

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An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / Henri Lombardi, Daniel Perrucci, Marie-Fran©ʹoise Roy.

Author/creator	Lombardi, Henri
Other author	Perrucci, Daniel.
Other author	Roy, M.-F. (Marie-Fran©ʹoise)
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2020.
Description	v, 125 pages ; 26 cm
Supplemental Content	Full text available from Memoirs of the American Mathematical Society
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Polynomials. Algebraic fields. Recursive functions.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 263 number 1277
Contents	Weak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex.
Abstract	"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2℗ø(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2020023856
ISBN	9781470441081 (paperback)
ISBN	(ebook)

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An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / Henri Lombardi, Daniel Perrucci, Marie-Fran©ʹoise Roy.

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