An algorithmic characterization
An algorithmic characterization
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算法表征
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发表时间：
2007
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通讯作者：
Y. Lequain
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作者：
Y. Lequain
设K是特征为零的域，d是K [X; Y 1，..]的导子。. .，Yn]的类型d =<$X + ∑ ni =1（ai Yi + bi）<$Yi，其中ai，bi ∈ K [X ].我们刻画了性质“d是K [X; Y 1，. . .，Yn]“，根据d的某个性质，可以有效地检查它是否满足的性质。我们应用我们的算法展示家庭的简单导子K [X; Y 1，. . .，Yn]，这与迄今为止所知的非常不同。我们还证明了我们的算法可以转化为一个有效地判定幂级数环K [[t]]中代数方程组{yi（t）= ai（t + α）yi（t）+ bi（t + α）} ni =1，α ∈ K，的解是否在K（t）上代数无关的算法.© 2007 Elsevier B. V.保留所有权利。MSC：小学：13.N.15;中学：13.P.99
Let K be a field of characteristic zero, d a derivation of K [X; Y1, . . . , Yn] of the type d = ∂X + ∑n i=1(ai Yi + bi )∂Yi with ai , bi ∈ K [X ] for every i . We characterize the property “d is a simple derivation of K [X; Y1, . . . , Yn]” in terms of a certain property of d, a property that one can effectively check for whether it is satisfied or not. We apply our algorithm to exhibit families of simple derivations of K [X; Y1, . . . , Yn] that are very different from what has been known until now. We also show that our algorithm can be traduced into one that determines effectively whether the solutions in the power series ring K [[t]] of the system of algebraic equations { y i (t) = ai (t + α)yi (t) + bi (t + α) }n i=1 , α ∈ K , are algebraically independent over K (t) or not. c © 2007 Elsevier B.V. All rights reserved. MSC: Primary: 13.N.15; secondary: 13.P.99