Numerical stability of Euclidean algorithm over ultrametric fields
نویسندگان
چکیده
منابع مشابه
Kac-Moody groups over ultrametric fields
The Kac-Moody groups studied here are the minimal (=algebraic) and split ones, as introduced by J. Tits in [8]. When they are defined over an ultrametric field, it seems natural to associate to them some analogues of the Bruhat-Tits buildings. Actually I came to this problem when I was trying to build new buildings of nondiscrete type. If G is a Kac-Moody group over an ultrametric field K, I wa...
متن کاملUltrametric sets in Euclidean point spaces
Finite sets S of points in a Euclidean space the mutual distances of which satisfy the ultrametric inequality (A;B) maxf (A;C); (C;B)g for all points in S are investigated and geometrically characterized. Inspired by results on ultrametric matrices and previous results on simplices, connections with so-called centered metric trees as well as with strongly isosceles right simplices are found. AM...
متن کاملThe Euclidean Algorithm in Cubic Number Fields
In this note we present algorithms for computing Euclidean minima of cubic number fields; in particular, we were able to find all normEuclidean cubic number fields with discriminants −999 < d < 104.
متن کاملStability of Linear-Quadratic Minimization over Euclidean Balls
Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...
متن کاملThe Euclidean Algorithm for Number Fields and Primitive Roots
Artin’s Primitive Root Conjecture. If a is not -1 or a square then there are infinitely many primes p such that a is a primitive root modulo p. In fact, for an explicit constant A(a) Artin conjectured that the number of primes p ≤ x such that a is a primitive root modulo p is ∼ A(a)x/ log x. Assuming the generalized Riemann hypothesis (GRH), Hooley proved this conjecture in 1967. In 1983 Gupta ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2017
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.989