Software for numerical algebraic geometry: a paradigm and progress towards its implementation

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Abstract

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.

[Uses Bertini v 1.0.1]

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Attribute NameValues
Creator
  • Charles Wampler

  • Andrew Sommese

  • Jonathan Hauenstein

Journal or Work Title
  • Software for algebraic geometry

First Page
  • 1

Last Page
  • 14

Publisher
  • Springer

Date Created
  • 2016-10-13

Bibliographic Citation
Language
  • English

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Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0N877QM

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