Homotopy techniques for multiplication modulo triangular sets
نویسندگان
چکیده
منابع مشابه
Homotopy techniques for multiplication modulo triangular sets
We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given to notably addition of a...
متن کاملHomotopy methods for multiplication modulo triangular sets
We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given to notably addition of a...
متن کاملComputing GCDs of polynomials modulo triangular sets
We present a modular algorithm for computing GCDs of univariate polynomials with coefficients modulo a zero-dimensional triangular set. Our algorithm generalizes previous work for computing GCDs over algebraic number fields. The main difficulty is when a zero divisor is encountered modulo a prime number. We give two ways of handling this: Hensel lifting, and fault tolerant rational reconstructi...
متن کاملRicci Curvature modulo Homotopy
This article is a report summarizing recent progress in the geometry of negative Ricci and scalar curvature. It describes the range of general existence results of such metrics on manifolds of dimension ≥ 3. Moreover it explains flexibility and approximation theorems for these curvature conditions leading to unexpected effects. For instance, we find that “modulo homotopy” (in a specified sense)...
متن کاملA Systolic Architecture for Modulo Multiplication
With the current advances in VLSI technology, traditional algorithms for Residue Number System (RNS) based architectures should be reevaluated to explore the new technology dimensions. In this brief, we introduce A @(log n ) algorithm for large moduli multiplication for RNS based architectures. A systolic array has been designed to perform the modulo multiplication Algorithm. The proposed modul...
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 of Symbolic Computation
سال: 2011
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2011.08.015