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TitleFast arithmetic for triangular sets: From theory to practice
Author(s) Xiaoliang Li, Marc Moreno Maza, Éric Schost
TypeArticle in Journal
AbstractWe 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 Monaganís modular GCD algorithm.
KeywordsFast polynomial arithmetic, Triangular set, High-performance computing
URL http://www.sciencedirect.com/science/article/pii/S0747717108001284
JournalJournal of Symbolic Computation
Pages891 - 907
NoteInternational Symposium on Symbolic and Algebraic Computation
Translation No
Refereed No