Implicitization Matrices in the Style of Sylvester with the Order of Bezout

Abstract

Resultants are the standard tool used to compute the implicit equation of a rational curve or surface. Here we present a new way to compute the implicit equation of a rational curve by taking the determinant of a matrix having the style of the Sylvester resultant but the size of the Bezout resultant. Thus the new method has the advantages of both resultant schemes, representing the implicit equation as the determinant of a matrix with simple linear entries and lots of zeros just like the Sylvester resultant, but with the same small size as the Bezout resultant.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP012012

Entities

People

  • Eng Wee Chionh
  • Ming Zhang
  • Ronald Goldman

Organizations

  • Rice University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Coefficients
  • Equations
  • Linear Algebra
  • Linear Systems
  • Polynomials
  • Rational Functions
  • Standards
  • Technical Information Centers
  • Universities

Fields of Study

  • Mathematics

Readers

  • Aerospace Research.
  • Approximation Theory.
  • Organizational Psychology.