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A probabilistic parallel modular algorithm for rational univariate representation
arXiv - CS - Symbolic Computation Pub Date : 2021-06-21 , DOI: arxiv-2106.10912
Bernard ParisseIF

This article does not introduce new mathematical ideas, it is more a state of the art June 2021 picture about solving polynomial systems efficiently by reconstructing a rational univariate representation with a very high probability of correctness using Groebner revlex computation, Berlekamp-Massey algorithm and Hankel linear system solving modulo several primes in parallel. This algorithm is implemented in Giac/Xcas since version 1.7.0-13, it has (June 2021) leading performances on multiple CPU, at least for an open-source software.

中文翻译:

一种用于有理单变量表示的概率并行模算法

本文没有介绍新的数学思想,它更像是 2021 年 6 月关于通过使用 Groebner revlex 计算、Berlekamp-Massey 算法和 Hankel 线性重构具有非常高正确概率的有理单变量表示来有效求解多项式系统的最新技术系统并行求解多个素数的模。该算法从 1.7.0-13 版本开始在 Giac/Xcas 中实现,它(2021 年 6 月)在多个 CPU 上具有领先的性能,至少对于开源软件而言是这样。
更新日期:2021-06-25
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