منابع مشابه
Encoding 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 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 کاملalgebraic 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)
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2017
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-017-9354-z