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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 Euler calculus ： ウィキペディア英語版 Euler calculus Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions〔Baryshnikov, Y.; Ghrist, R. (Euler integration for definable functions ), ''Proc. National Acad. Sci.'', 107(21), 9525–9530, 25 May 2010.〕 by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem. It was introduced independently by Pierre Schapira〔Schapira, P. "Cycles Lagrangiens, fonctions constructibles et applications", Seminaire EDP, Publ. Ecole Polytechnique (1988/89)〕〔Schapira, P. (Operations on constructible functions ), ''J. Pure Appl. Algebra'' 72, 1991, 83–93.〕〔Schapira, Pierre. (Tomography of constructible functions ), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes Lecture Notes in Computer Science, 1995, Volume 948/1995, 427–435, 〕 and Oleg Viro〔Viro, O. (Some integral calculus based on Euler characteristic ), ''Lecture Notes in Math.'', vol. 1346, Springer-Verlag, 1988, 127–138.〕 in 1988, and is useful for enumeration problems in computational geometry and sensor networks.〔Baryshnikov, Y.; Ghrist, R. (Target enumeration via Euler characteristic integrals ), SIAM ''J. Appl. Math.'', 70(3), 825–844, 2009.〕 ==See also== *Topological data analysis 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「Euler calculus」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.