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:

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Xin Li, Marc Moreno Maza, Éric Schost
• Keywords: Direct Recursive Approach, ISSAC 2007, Modular Gcd Algorithm, Univariate Euclidean Division