翻訳と辞書 Words near each other ・ Laurent Paquin ・ Laurent Pardo ・ Laurent Pariente ・ Laurent Pellet ・ Laurent Pelly ・ Laurent Percerou ・ Laurent Petitgirard ・ Laurent Petitguillaume ・ Laurent Picard ・ Laurent Piche ・ Laurent Pichon ・ Laurent Pillon ・ Laurent Pionnier ・ Laurent Pokou ・ Laurent Poliquin ・ Laurent polynomial ・ Laurent Porchier ・ Laurent Prades ・ Laurent Quievreux ・ Laurent Quintreau ・ Laurent Recouderc ・ Laurent Riboulet ・ Laurent Rioux ・ Laurent Robert ・ Laurent Robinson ・ Laurent Robuschi ・ Laurent Rodriguez ・ Laurent Romejko ・ Laurent Ronde ・ Laurent Roussey 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 Laurent polynomial ： ウィキペディア英語版 Laurent polynomial In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field $\backslash mathbb$ is a linear combination of positive and negative powers of the variable with coefficients in $\backslash mathbb$. Laurent polynomials in ''X'' form a ring denoted $\backslash mathbb$(''X''−1 ). They differ from ordinary polynomials in that they may have terms of negative degree. The construction of Laurent polynomials may be iterated, leading to the ring of Laurent polynomials in several variables. == Definition == A Laurent polynomial with coefficients in a field $\backslash mathbb$ is an expression of the form : $p\; =\; \backslash sum\_k\; p\_k\; X^k,\; \backslash quad\; p\_k\backslash in\; \backslash mathbb$ where ''X'' is a formal variable, the summation index ''k'' is an integer (not necessarily positive) and only finitely many coefficients ''p''''k'' are non-zero. Two Laurent polynomials are equal if their coefficients are equal. Such expressions can be added, multiplied, and brought back to the same form by reducing similar terms. Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of ''X'' can be present: :$\backslash left(\backslash sum\_i\; a\_iX^i\backslash right)\; +\; \backslash left(\backslash sum\_i\; b\_iX^i\backslash right)\; =$ \sum_i (a_i+b_i)X^i and :$\backslash left(\backslash sum\_i\; a\_iX^i\backslash right)\; \backslash cdot\; \backslash left(\backslash sum\_j\; b\_jX^j\backslash right)\; =$ \sum_k \left(\sum_ a_i b_j\right)X^k. Since only finitely many coefficients ''a''''i'' and ''b''''j'' are non-zero, all sums in effect have only finitely many terms, and hence represent Laurent polynomials. 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「Laurent 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.