منابع مشابه
Efficient Arithmetic Modulo Minimal Redundancy Cyclotomic Primes
We introduce a family of prime numbers that we refer to as Minimal Redundancy Cyclotomic Primes (MRCPs). The form of MRCPs is such that when using the field representation and multiplication algorithm we present, multiplication modulo these primes can be up to twice as efficient as multiplication of integer residues. This article provides a comprehensive theoretical framework for the use of MRC...
متن کاملCyclotomic Invariants for Primes to One Million
Our recent computation of cyclotomic invariants for primes between 125000 and 150000 was extended to one million. No new phenomena appear. This note is a sequel to our recent report [2] on the computation of certain cyclotomic invariants for primes p between 125000 and 150000. That work was based on the table of irregular primes supplied by Tanner and Wagstaff (see [4]). Meanwhile, the extensio...
متن کاملCyclotomic structures on root lattices
The centralizer C(w) of an element w in a Weyl group W plays an important role in the structure and representation theory of split reductive groups G over finite and p-adic fields k, where W is the absolute Weyl group of G. If k is finite, this is well-known: the element w determines a maximal ktorus Tw ⊂ G and C(w) may be identified with the k-rational points in the Weyl group W (Tw, G) of Tw ...
متن کاملBad Primes in Computational Algebraic Geometry
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method is guaranteed to work if we use a sufficiently large set of good primes. In many applications, however, there is no efficient way of excluding bad primes. In...
متن کاملThe use of bad primes in rational reconstruction
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction. Successively enlarging the set of primes if needed, this method is guaranteed to work if we restrict ourselves to “good” primes. Depending on the particular app...
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: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.11.020