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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 Division polynomials ： ウィキペディア英語版 Division polynomials In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm. == Definition == The set of division polynomials is a sequence of polynomials in $\backslash mathbb()$ with $x,\; y,\; A,\; B$ free variables that is recursively defined by: ::$\backslash psi\_\; =\; 0$ ::$\backslash psi\_\; =\; 1$ ::$\backslash psi\_\; =\; 2y$ ::$\backslash psi\_\; =\; 3x^\; +\; 6Ax^\; +\; 12Bx\; -\; A^$ ::$\backslash psi\_\; =\; 4y(x^\; +\; 5Ax^\; +\; 20Bx^\; -\; 5A^x^\; -\; 4ABx\; -\; 8B^\; -\; A^)$ ::$\backslash vdots$ ::$\backslash psi\_\; =\; \backslash psi\_\; \backslash psi\_^\; -\; \backslash psi\_\; \backslash psi\; ^\_\; \backslash text\; m\; \backslash geq\; 2$ ::$\backslash psi\_\; =\; \backslash left\; (\; \backslash frac\; \backslash right\; )\; \backslash cdot\; (\; \backslash psi\_\backslash psi^\_\; -\; \backslash psi\_\; \backslash psi\; ^\_)\; \backslash text\; m\; \backslash geq\; 3$ The polynomial $\backslash psi\_n$ is called the ''n''th division polynomial. 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「Division polynomials」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.