منابع مشابه
ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملEffective Algebraic Power Series
The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series.
متن کاملEncoding Algebraic Power Series
The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes of the reduced standard basis of the ideal can be constructed effectively.
متن کاملAlgebraic Diagonals and Walks: Algorithms, Bounds, Complexity
The diagonal of a multivariate power series F is the univariate power series Diag F generated by the diagonal terms of F . Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. We study algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1987
ISSN: 0022-314X
DOI: 10.1016/0022-314x(87)90095-3