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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stengle's Positivstellensatz ： ウィキペディア英語版 Stengle's Positivstellensatz In real semialgebraic geometry, Stengle's (German for "positive-locus-theorem" – see ''Satz'') characterizes polynomials that are positive on a semialgebraic set, which is defined by systems of inequalities of polynomials with real coefficients, or more generally, coefficients from any real closed field. It can be thought of as an ordered analogue of Hilbert's Nullstellensatz. It was proved by Jean-Louis Krivine and then rediscovered by Gilbert Stengle. ==Statement== Let be a real closed field, and a finite set of polynomials over in variables. Let be the semialgebraic set :$W=\backslash ,$ and let be the cone generated by (i.e., the subsemiring of () generated by and arbitrary squares). Let  ∈ () be a polynomial. Then :$\backslash forall\; x\backslash in\; W\backslash ;p(x)>0$ if and only if $\backslash exists\; f\_1,f\_2\backslash in\; C\backslash ;pf\_1=1+f\_2$. The ''weak '' is the following variant of the . Let be a real-closed field, and , , and finite subsets of (). Let be the cone generated by , and the ideal generated by . Then :$\backslash =\backslash emptyset$ if and only if :$\backslash exists\; f\backslash in\; C,g\backslash in\; I,n\backslash in\backslash mathbb\; N\backslash ;f+g+\backslash left(\backslash prod\; H\backslash right)^=0.$ (Unlike , the "weak" form actually includes the "strong" form as a special case, so the terminology is a misnomer.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stengle's Positivstellensatz」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.