|Modpn is a C library offering highly optimized
routines for multivariate polynomials arithmetic in prime
characteristic. By bridging these low-level and architecture-aware
routines to high-level mathematical code, large speed-up factors can be
obtained. This is case, for instance, with the module
FastArithmeticTools of the RegularChains library in Maple 13, which
provides commands for solving systems of non-linear equations.
In this talk, we illustrate how Modpn can be used to efficiently
implement modular methods in Maple and take advantage of FFT-based and
SLP-based polynomial arithmetic. One goal is to show how to handle the
technical difficulties arising in this framework, such as
data-conversion overheads, choice of characteristics. We also discuss
the determination of thresholds between mixed code and non-mixed code.
We conclude by an overview
of the current development for multi-core support