翻訳と辞書 Words near each other ・ Different World (song) ・ Different Worlds ・ Different Worlds Publications ・ Different Yet the Same ・ Differentia ・ Differentiable function ・ Differentiable manifold ・ Differentiable stack ・ Differential ・ Differential (infinitesimal) ・ Differential (mathematics) ・ Differential (mechanical device) ・ Differential Ability Scales ・ Differential accumulation ・ Differential adhesion hypothesis ・ Differential algebra ・ Differential algebraic equation ・ Differential algebraic geometry ・ Differential algebraic group ・ Differential amplifier ・ Differential analyser ・ Differential and absolute ground rent ・ Differential association ・ Differential backup ・ Differential calculus ・ Differential calculus over commutative algebras ・ Differential capacitance ・ Differential centrifugation ・ Differential coding ・ Differential coefficient 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 Differential algebra ： ウィキペディア英語版 Differential algebra In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule. A natural example of a differential field is the field of rational functions ''C''(''t'') in one variable, over the complex numbers, where the derivation is the differentiation with respect to ''t''. Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use for an algebraic study of the differential equations. Differential algebra was introduced by Joseph Ritt. ==Differential ring== A ''differential ring'' is a ring ''R'' equipped with one or more ''derivations'', that is additive homomorphisms :$\backslash partial:R\; \backslash to\; R\backslash ,$ such that each derivation ∂ satisfies the Leibniz product rule :$\backslash partial(r\_1\; r\_2)=(\backslash partial\; r\_1)\; r\_2\; +\; r\_1\; (\backslash partial\; r\_2),\backslash ,$ for every $r\_1,\; r\_2\; \backslash in\; R$. Note that the ring could be noncommutative, so the somewhat standard ''d(xy) = xdy + ydx'' form of the product rule in commutative settings may be false. If $M:R\; \backslash times\; R\; \backslash to\; R$ is multiplication on the ring, the product rule is the identity :$\backslash partial\; \backslash circ\; M\; =$ M \circ (\partial \times \operatorname) + M \circ (\operatorname \times \partial). where $f\backslash times\; g$ means the function which maps a pair $(x,y)$ to the pair $(f(x),g(y))$. 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「Differential algebra」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.