LEADER 02761nam 2200517 450 001 9910806857203321 005 20200817175903.0 010 $a1-4704-5662-1 035 $a(CKB)4100000011040076 035 $a(MiAaPQ)EBC6176749 035 $a(RPAM)21609888 035 $a(PPN)250211394 035 $a(EXLCZ)994100000011040076 100 $a20200817d2020 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem /$fHenri Lombardi, Daniel Perrucci, Marie-Franc?oise Roy 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2020. 215 $a1 online resource (138 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 263 311 $a1-4704-4108-X 320 $aIncludes bibliographical references. 327 $aWeak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex. 330 $a"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 263. 606 $aPolynomials 606 $aAlgebraic fields 606 $aRecursive functions 615 0$aPolynomials. 615 0$aAlgebraic fields. 615 0$aRecursive functions. 676 $a512.9422 686 $a12D15$a14P99$a13J30$2msc 700 $aLombardi$b Henri$0755733 702 $aPerrucci$b Daniel 702 $aRoy$b M.-F$g(Marie-Franc?oise), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910806857203321 996 $aAn elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem$93941084 997 $aUNINA