Software for numerical algebraic geometry: a paradigm and progress towards its implementation
Software for numerical algebraic geometry: a paradigm and progress towards its implementation
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DOI：
10.1007/978-0-387-78133-4_1
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Daniel J. Bates;J. Hauenstein;A. Sommese;C. Wampler
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文献类型：
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作者：
Daniel J. Bates;J. Hauenstein;A. Sommese;C. Wampler
虽然数值方法找到所有孤立的解决方案的非线性系统的多元多项式可以追溯到30年前，它只是在过去的十年中，数值方法已被设计用于计算和操作的代数集来自多项式系统的复数。总的来说，这些算法和基本理论被称为数值代数几何。有几个软件包能够进行一些运算的数值代数几何，但没有一个包提供所有这些功能。本文包含一个枚举的操作，一个理想的软件包在这一领域将允许。贝尔蒂尼，在这一领域的最新发布的软件包，目前和即将到来的能力也进行了说明。
Though numerical methods to find all the isolated solutions of nonlinear systems of multivariate polynomials go back 30 years, it is only over the last decade that numerical methods have been devised for the computation and manipulation of algebraic sets coming from polynomial systems over the complex numbers. Collectively, these algorithms and the underlying theory have come to be known as numerical algebraic geometry. Several software packages are capable of carrying out some of the operations of numerical algebraic geometry, although no one package provides all such capabilities. This paper contains an enumeration of the operations that an ideal software package in this field would allow. The current and upcoming capabilities of Bertini, the most recently released package in this field, are also described.