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2007
Springer

Fast arithmetic for triangular sets: from theory to practice

11 years 5 months ago
Fast arithmetic for triangular sets: from theory to practice
We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean division, we obtain theoretical and practical improvements over a direct recursive approach; for a family of special cases, we reach quasi-linear complexity. The main outcome we have in mind is the acceleration of higher-level algorithms, by interfacing our low-level implementation with languages such as AXIOM or Maple. We show the potential for huge speed-ups, by comparing two AXIOM implementations of van Hoeij and Monagan’s modular GCD algorithm. Categories and Subject Descriptors:
Xin Li, Marc Moreno Maza, Éric Schost
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where ISSAC
Authors Xin Li, Marc Moreno Maza, Éric Schost
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