Implementation techniques for fast polynomial arithmetic in a high-level programming environment

Though there is increased activity in the implementation of asymptotically fast polynomial arithmetic, little is reported on the details of such effort. In this paper, we discuss how we achieve high performance in implementing some well-studied fast algorithms for polynomial arithmetic in two high-level programming environments, AXIOM and Aldor. Two approaches are investigated. With Aldor we rely only on high-level generic code, whereas with AXIOM we endeavor to mix high-level, middle-level and low-level specialized code. We show that our implementations are satisfactory compared with other known computer algebra systems or libraries such as Magma v2.11-2 and NTL v5.4. Categories and Subject Descriptors