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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 Quasi-polynomial ： ウィキペディア英語版 Quasi-polynomial In mathematics, a quasi-polynomial (pseudo-polynomial) is a generalization of polynomials. While the coefficients of a polynomial come from a ring, the coefficients of quasi-polynomials are instead periodic functions with integral period. Quasi-polynomials appear throughout much of combinatorics as the enumerators for various objects. A quasi-polynomial can be written as $q(k)\; =\; c\_d(k)\; k^d\; +\; c\_(k)\; k^\; +\; \backslash cdots\; +\; c\_0(k)$, where $c\_(k)$ is a periodic function with integral period. If $c\_d(k)$ is not identically zero, then the degree of ''q'' is ''d''. Equivalently, a function $f\; \backslash colon\; \backslash mathbb\; \backslash to\; \backslash mathbb$ is a quasi-polynomial if there exist polynomials $p\_0,\; \backslash dots,\; p\_$ such that $f(n)\; =\; p\_i(n)$ when $n\; \backslash equiv\; i\; \backslash bmod\; s$. The polynomials $p\_i$ are called the constituents of ''f''. ==Examples== * Given a ''d''-dimensional polytope ''P'' with rational vertices $v\_1,\backslash dots,v\_n$, define ''tP'' to be the convex hull of $tv\_1,\backslash dots,tv\_n$. The function $L(P,t)\; =\; \backslash \#(tP\; \backslash cap\; \backslash mathbb^d)$ is a quasi-polynomial in ''t'' of degree ''d''. In this case, ''L(P,t)'' is a function $\backslash mathbb\; \backslash to\; \backslash mathbb$. This is known as the Ehrhart quasi-polynomial, named after Eugène Ehrhart. * Given two quasi-polynomials ''F'' and ''G'', the convolution of ''F'' and ''G'' is :$(F$ *G)(k) = \sum_^k F(m)G(k-m) which is a quasi-polynomial with degree $\backslash le\; \backslash deg\; F\; +\; \backslash deg\; G\; +\; 1.$ 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「Quasi-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.