P-adic Root Isolation
نویسندگان
چکیده
We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method wrt. the coefficients of f and the primes p. Our method thus provides information analogous to that provided by well-established real methods as, e.g., Cauchy bounds and Sturm sequences over the reals. [email protected], http://www.fmi.uni-passau.de/ ̃sturm/ [email protected]
منابع مشابه
Some bounds on unitary duals of classical groups - non-archimeden case
We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups. Roughly, they can show up only if the central character of the inducing irreducible cuspidal representation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients...
متن کامل$p$-adic Dual Shearlet Frames
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...
متن کاملp-Adic description of Higgs mechanism I: p-Adic square root and p-adic light cone
This paper is the first one in the series devoted to the calculation of particle mass spectrum in Topological GeometroDynamics. In this paper p-adic conformal field theory limit of TGD is formulated. TGD Universe is critical at quantum level and the idea is to realize criticality via conformal invariance. Ordinary real numbers do not allow this but if one assumes that in long length scales p-ad...
متن کاملDwork ’ s conjecture on unit root zeta functions
In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic continuation of Professor Bernard Dwork’s unit root zeta function attached to an ordinary family of algebraic varieties defined over a finite field of characteristic p. After his pioneer p-adic investigation of the Weil conjectures on the zeta function of an algebraic variety over a finite fi...
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004