Real Numerical Algebraic Geometry: Finding All Real Solutions of a Polynomial System

Abstract

This project resulted in software and algorithms for computing the real solution of polynomial systems contained within complex curves and surfaces. The primary product was Bertini Real, a publicly available software package for these computations. Secondary products included four articles, all in progress. These articles document the algorithms developed during the reporting period, including (1) a complete algorithm in the case of complex surfaces with no restricitons on the type of surface; (2) a technical article on the theory underlying and algorithm for finding critical points; (3) an article on Bertini Real; and (4) an article on the real numerical irreducible decomposition.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2014
Accession Number
ADA597283

Entities

People

  • Andrew J. Sommese
  • Charles W. Wampler
  • Daniel A. Brake
  • Daniel J. Bates
  • Jonathan D Hauenstein
  • Wenrui Hao

Organizations

  • Colorado State University

Tags

Communities of Interest

  • Air Platforms
  • Sensors

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algebraic Geometry
  • Algorithms
  • Computations
  • Decomposition
  • Geometry
  • Government Procurement
  • Governments
  • Mathematics
  • Military Research
  • Numbers
  • Polynomials
  • Software Development
  • Three Dimensional
  • Two Dimensional
  • United States

Readers

  • Computer Vision.
  • Mathematical Modeling and Probability Theory.
  • Technical Research and Report Writing.