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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 Tate's algorithm ： ウィキペディア英語版 Tate's algorithm In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve ''E'' over $\backslash mathbb$, or more generally an algebraic number field, and a prime or prime ideal ''p''. It returns the exponent ''f''''p'' of ''p'' in the conductor of ''E'', the type of reduction at ''p'', the local index : $c\_p=(),$ where $E^0(\backslash mathbb\_p)$ is the group of $\backslash mathbb\_p$-points whose reduction mod ''p'' is a non-singular point. Also, the algorithm determines whether or not the given integral model is minimal at ''p'', and, if not, returns an integral model with integral coefficients for which the valuation at ''p'' of the discriminant is minimal. Tate's algorithm also gives the structure of the singular fibers given by the Kodaira symbol or Néron symbol, for which, see elliptic surfaces: in turn this determines the exponent ''f''''p'' of the conductor ''E''. Tate's algorithm can be greatly simplified if the characteristic of the residue class field is not 2 or 3; in this case the type and ''c'' and ''f'' can be read off from the valuations of ''j'' and Δ (defined below). Tate's algorithm was introduced by as an improvement of the description of the Néron model of an elliptic curve by . ==Notation== Assume that all the coefficients of the equation of the curve lie in a complete discrete valuation ring ''R'' with perfect residue field and maximal ideal generated by a prime π. The elliptic curve is given by the equation :$y^2+a\_1xy+a\_3y\; =\; x^3+a\_2x^2+a\_4x+a\_6.\backslash$ Define: :$a\_=a\_i/\backslash pi^m$ :$b\_2=a\_1^2+4a\_2$ :$b\_4=a\_1a\_3+2a\_4^\{\}$ :$b\_6=a\_3^2+4a\_6$ :$b\_8=a\_1^2a\_6-a\_1a\_3a\_4+4a\_2a\_6+a\_2a\_3^2-a\_4^2$ :$c\_4=b\_2^2-24b\_4$ :$c\_6=-b\_2^3+36b\_2b\_4-216b\_6$ :$\backslash Delta=-b\_2^2b\_8-8b\_4^3-27b\_6^2+9b\_2b\_4b\_6$ :$j=c\_4^3/\backslash Delta.$ 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「Tate's algorithm」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.