翻訳と辞書 Words near each other ・ Tarskavaig ・ Tarski monster group ・ Tarski's axiomatization of the reals ・ Tarski's axioms ・ Tarski's circle-squaring problem ・ Tarski's exponential function problem ・ Tarski's high school algebra problem ・ Tarski's plank problem ・ Tarski's problem ・ Tarski's theorem ・ Tarski's theorem about choice ・ Tarski's undefinability theorem ・ Tarski's World ・ Tarski–Grothendieck set theory ・ Tarski–Kuratowski algorithm ・ Tarski–Seidenberg theorem ・ Tarsky ・ Tarsky District ・ Tarsnap ・ Tarsney ・ Tarso ・ Tarso Genro ・ Tarso Marques ・ Tarso Toh ・ Tarso Voon ・ Tarsocera ・ Tarsocera cassina ・ Tarsocera cassus ・ Tarsocera dicksoni ・ Tarsocera fulvina Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tarski–Seidenberg theorem ： ウィキペディア英語版 Tarski–Seidenberg theorem In mathematics, the Tarski–Seidenberg theorem states that a set in (''n'' + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto ''n''-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities. The theorem — also known as the Tarski–Seidenberg projection property — is named after Alfred Tarski and Abraham Seidenberg. It implies that quantifier elimination is possible over the reals, that is that every formula constructed from polynomial equations and inequalities by logical connectors ∨ (''or''), ∧ (''and''), ¬ (''not'') and quantifiers ∀ (''for all''), ∃ (''exists'') is equivalent with a similar formula without quantifiers. An important consequence is the decidability of the theory of real-closed fields. ==Statement== A semialgebraic set in R''n'' is a finite union of sets defined by a finite number of polynomial equations and inequalities, that is by a finite number of statements of the form :$p(x\_1,\backslash ldots,x\_n)=0\backslash ,$ and :$q(x\_1,\backslash ldots,x\_n)>0\backslash ,$ for polynomials ''p'' and ''q''. We define a projection map ''π'' : R''n''+1 → R''n'' by sending a point (''x''1,...,''x''''n'',''x''''n''+1) to (''x''1,...,''x''''n''). Then the Tarski–Seidenberg theorem states that if ''X'' is a semialgebraic set in R''n''+1 for some ''n'' > 1, then ''π''(''X'') is a semialgebraic set in R''n''. 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「Tarski–Seidenberg theorem」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.