An elementary approach to subresultants theory

Authors:
M'hammed El Kahoui
Affiliations:
Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Boulevard My Abdellah, P.O. Box 2390, Marrakech, Morocco
Venue:
Journal of Symbolic Computation
Year:
2003

Citing 11
Cited 6

The Habicht approach to subresultants

Journal of Symbolic Computation
Semi-algebraic complexity of quotients and sign determination of remainders

Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Subresultants under composition

Journal of Symbolic Computation
Asymptotically fast computation of subresultants

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Modern computer algebra

Modern computer algebra
Subresultants and Reduced Polynomial Remainder Sequences

Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants

Journal of the ACM (JACM)
New structure theorem for subresultants

Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Sylvester—Habicht sequences and fast Cauchy index computation

Journal of Symbolic Computation
Subresultants Revisited

LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Differential Resultants and Subresultants

FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory

Exact, efficient, and complete arrangement computation for cubic curves

Computational Geometry: Theory and Applications
Real Algebraic Numbers: Complexity Analysis and Experimentation

Reliable Implementation of Real Number Algorithms: Theory and Practice
Computations modulo regular chains

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Exact, efficient, and complete arrangement computation for cubic curves

Computational Geometry: Theory and Applications
Birational properties of the gap subresultant varieties

Journal of Symbolic Computation
Separating linear forms for bivariate systems

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we give an elementary approach to univariate polynomial subresultants theory. Most of the known results of subresultants are recovered, some with more precision, without using Euclidean divisions or existence of roots for univariate polynomials. The main contributions of this paper are not new results on subresultants, but rather extensions of the main results over integral rings to arbitrary commutative rings.