SI2-SSE: Collaborative Proposal: Symbolic-Numeric Approaches to Polynomials

SI2-SSE：协作提案：多项式的符号数值方法

• 批准号: 1440583
• 负责人: Jonathan Hauenstein
• 金额: $ 15万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2014-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1440583&HistoricalAwards=false
• 关键词: SI2; SSE; Collaborative; Proposal; Symbolic

Polynomial systems arise naturally in many areas of human endeavor. These include the modeling of tumor growth; the design of robotic devices; chemical systems arising in areas ranging from combustion to blood clotting; assorted problems in physics; plus many areas with mathematics. The solution of the polynomial systems answers questions critical to these endeavors. This research will be devoted to developing the next generation of Bertini, an open source software package, which has been used successfully by many researchers on many problems, which include all those mentioned above.Bertini will be rewritten in C++ to be scriptable and modular, which will allow it to be interfaced transparently with symbolic software. The new Bertini will include tools allowing the user to construct and manipulate homotopies based on the output of Bertini. A major focus of the research will be given to systems of polynomials arising from the discretization of systems of differential equations. The great challenge of these very large systems of polynomials is balanced by the great potential impact new efficient and robust methods of solution will have.

多项式系统自然出现在人类努力的许多领域。这些包括肿瘤生长的建模；机器人设备的设计；从燃烧到血液凝结的地区产生的化学系统；物理学中的各种问题；加上许多数学领域。多项式系统的解决方案回答了对这些努力至关重要的问题。这项研究将致力于开发下一代Be​​rtini，Bertini是一个开源软件包，许多研究人员成功地使用了许多问题，其中包括上面提到的所有问题。Bertini将在C ++中重写可脚本化和模块化，这将允许它与符号软件透明地连接。新的Bertini将包括允许用户根据Bertini的输出来构建和操纵同质的工具。研究的重点将放在由微分方程系统离散化的多项式系统上。这些非常大的多项式系统的巨大挑战是通过新的有效和强大的解决方案的巨大影响来平衡的。