Solving Polynomial Systems with phcpy
Solving Polynomial Systems with phcpy
复制标题
使用 phcpy 求解多项式系统
DOI：
10.25080/majora-7ddc1dd1-009
复制
发表时间：
2019
期刊：
影响因子：
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通讯作者：
J. Verschelde
中科院分区：
文献类型：
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作者：
Jasmine Otto;A. Forbes;J. Verschelde
在机械系统的设计和非线性生物动力学的相空间分析中，经常需要求解多个变量的多项式系统。可靠的，准确的，全面的数值解决方案是通过PHCpack，一个自由开源软件包求解多项式系统与同伦延。本文探讨了PHCpack的脚本接口phcpy在过去五年中取得的新进展。例如，phcpy现在可以通过具有Python2、Python3和SageMath内核的JupyterHub服务器在线获得。由于小系统是通过物理实时求解的，因此适合通过笔记本界面进行交互式探索。同时，phcpy支持GPU并行化，提高求解更大多项式系统的速度和质量。在STEM中的各种模型设计和分析问题中，经常会出现某些类型的多项式系统，这是物理学非常适合的。
The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical solutions are available through PHCpack, a FOSS package for solving polynomial systems with homotopy continuation. This paper explores new developments in phcpy, a scripting interface for PHCpack, over the past five years. For instance, phcpy is now available online through a JupyterHub server featuring Python2, Python3, and SageMath kernels. As small systems are solved in real-time by phcpy, they are suitable for interactive exploration through the notebook interface. Meanwhile, phcpy supports GPU parallelization, improving the speed and quality of solutions to much larger polynomial systems. From various model design and analysis problems in STEM, certain classes of polynomial system frequently arise, to which phcpy is well-suited.