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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 Hasse principle ： ウィキペディア英語版 Hasse principle In mathematics, Helmut Hasse's local-global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the ''p''-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers ''and'' in the ''p''-adic numbers for each prime ''p''. ==Intuition== Given a polynomial equation with rational coefficients, if it has rational solution, then this also yields a real solution and a ''p''-adic solution, as the rationals embed in the reals and ''p''-adics: a global solution yields local solutions at each prime. The Hasse principle asks when the reverse can be done, or rather, asks what the obstruction is: when can you patch together solutions over the reals and ''p''-adics to yield a solution over the rationals: when can local solutions be joined to form a global solution? One can ask this for other rings or fields: integers, for instance, or number fields. For number fields, rather than reals and ''p''-adics, one uses complex embeddings and $\backslash mathfrak\; p$-adics, for prime ideals $\backslash mathfrak\; p$. 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「Hasse principle」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.