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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 Factor base ： ウィキペディア英語版 Factor base In computational number theory, a factor base is a small set of prime numbers commonly used as a mathematical tool in algorithms involving extensive sieving for potential factors of a given integer. ==Usage in factoring algorithms== A factor base is a relatively small set of distinct prime numbers ''P'', sometimes together with -1. Say we want to factorize an integer ''n''. We generate, in some way, a large number of integer pairs (''x'', ''y'') for which $x\; \backslash neq\; \backslash pm\; y$, $x^2\; \backslash equiv\; y^2\; \backslash pmod$, and $x^2\; \backslash pmod\; \backslash texty^2\; \backslash pmod$ can be completely factorized over the chosen factor base—that is, all their prime factors are in ''P''. In practice, several integers ''x'' are found such that $x^2\; \backslash pmod$ has all of its prime factors in the pre-chosen factor base. We represent each $x^2\; \backslash pmod$ expression as a vector of a matrix with integer entries being the exponents of factors in the factor base. Linear combinations of the rows corresponds to multiplication of these expressions. A linear dependence relation mod 2 among the rows leads to a desired congruence $x^2\; \backslash equiv\; y^2\; \backslash pmod$. This essentially reformulates the problem into a system of linear equations, which can be solved using numerous methods such as Gaussian elimination; in practice advanced methods like the block Lanczos algorithm are used, that take advantage of certain properties of the system. This congruence may generate the trivial $\backslash textstyle\; n\; =\; 1\; \backslash cdot\; n$; in this case we try to find another suitable congruence. If repeated attempts to factor fail we can try again using a different factor base. 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「Factor base」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.