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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 acnode ： ウィキペディア英語版 acnode An acnode is an isolated point not on a curve, but whose coordinates satisfy the equation of the curve. The term "isolated point or hermit point" is an equivalent term. Acnodes are commonly found in the study of algebraic curves over fields which are not algebraically closed, defined as the zero set of a polynomial of two variables. For example the equation :$f(x,y)=y^2+x^2-x^3=0\backslash ;$ has an acnode at the origin of $\backslash mathbb^2$, because it is equivalent to :$y^2\; =\; x^2\; (x-1)$ and $x^2(x-1)$ is non-negative when $x$ ≥ 1 and when $x\; =\; 0$. Thus, over the ''real'' numbers the equation has no solutions for except for (0, 0). In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. An acnode is a singularity of the function, where both partial derivatives $\backslash partial\; f\backslash over\; \backslash partial\; x$ and $\backslash partial\; f\backslash over\; \backslash partial\; y$ vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite. Hence the function has a local minimum or a local maximum. ==See also== *Singular point of a curve *Crunode *Cusp *Tacnode 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「acnode」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.