منابع مشابه
Resultants and subresultants of p-adic polynomials
We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are highly unstable on average and we explain, in many cases, how one can stabilize them without sacrifying the complexity. On the way, we completely determine the d...
متن کاملMeasurable Dynamics of Simple p-adic Polynomials
The p-adic numbers have many fascinating properties that are different from those of the real numbers. These properties are a consequence of the fact that the distance in the p-adics is measured using a non-Archimedian absolute value or norm. In this article we study the dynamics of algebraically defined transformations on the p-adics and see that there is a strong connection between the topolo...
متن کاملFactoring polynomials over p-adic elds
We give an eecient algorithm for factoring polynomials over nite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov's random polynomial-time algorithm, and is suitable for practical implementation.
متن کاملCharacteristic Polynomials of p-adic Matrices
We analyze the precision of the characteristic polynomial χ(A) of an n × n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p), we give a criterion (checkable in time O (̃n)) for χ(A) to have precision exactly O(p). We also give a O (̃n) algorithm for determining the optimal precision when the criterion is not satisfied, and give examp...
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2016
ISSN: 0019-3577
DOI: 10.1016/j.indag.2015.12.003