翻訳と辞書 Words near each other ・ Bernstein Prize ・ Bernstein set ・ Bernstein v. United States ・ Bernstein's constant ・ Bernstein's Fish Grotto ・ Bernstein's inequality (mathematical analysis) ・ Bernstein's problem ・ Bernstein's theorem ・ Bernstein's theorem (approximation theory) ・ Bernstein's theorem (polynomials) ・ Bernstein's theorem on monotone functions ・ Bernstein-Rein ・ Bernstein/Beethoven ・ Bernstein–Kushnirenko theorem ・ Bernstein–Mahler cycle ・ Bernstein–Sato polynomial ・ Bernstein–von Mises theorem ・ Bernstein–Zelevinsky classification ・ Bernstorf ・ Bernstorfer pond ・ Bernstorff ・ Bernstorff Palace ・ Bernstorffstøtten ・ Bernstorffsvej station ・ Bernt ・ Bernt A. Nissen ・ Bernt Albert ・ Bernt Andersson ・ Bernt Anker ・ Bernt Arne Lynge Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bernstein–Sato polynomial ： ウィキペディア英語版 Bernstein–Sato polynomial In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by and , . It is also known as the b-function, the b-polynomial, and the Bernstein polynomial, though it is not related to the Bernstein polynomials used in approximation theory. It has applications to singularity theory, monodromy theory and quantum field theory. gives an elementary introduction, and and give more advanced accounts. ==Definition and properties== If ''ƒ''(''x'') is a polynomial in several variables then there is a non-zero polynomial ''b''(''s'') and a differential operator ''P''(''s'') with polynomial coefficients such that :$P(s)f(x)^\; =\; b(s)f(x)^s.\; \backslash ,$ The Bernstein–Sato polynomial is the monic polynomial of smallest degree amongst such ''b''(''s''). Its existence can be shown using the notion of holonomic D-modules. proved that all roots of the Bernstein–Sato polynomial are negative rational numbers. The Bernstein–Sato polynomial can also be defined for products of powers of several polynomials . In this case it is a product of linear factors with rational coefficients. generalized the Bernstein–Sato polynomial to arbitrary varieties. Note, that the Bernstein–Sato polynomial can be computed algorithmically. However, such computations are hard in general. There are implementations of related algorithms in computer algebra systems RISA/Asir, Macaulay2 and SINGULAR. presented algorithms to compute the Bernstein–Sato polynomial of an affine variety together with an implementation in the computer algebra system SINGULAR. described some of the algorithms for computing Bernstein–Sato polynomials by computer. 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「Bernstein–Sato polynomial」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.