A subresultant theory for multivariate polynomials
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Solutions of systems of algebraic equations and linear maps on residue class rings
Journal of Symbolic Computation
Algorithms for intersecting parametric and algebraic curves II: multiple intersections
Graphical Models and Image Processing
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Symbolic and numeric methods for exploiting structure in constructing resultant matrices
Journal of Symbolic Computation
Hybrid sparse resultant matrices for bivariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Generalized Characteristic Polynomials
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
The resultant of an unmixed bivariate system
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Inversion of parameterized hypersurfaces by means of subresultants
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The Computational Complexity of the Chow Form
Foundations of Computational Mathematics
Subresultants and generic monomial bases
Journal of Symbolic Computation
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A general subresultant method is introduced to compute elements of a given ideal with few terms and bounded coefficients. This subresultant method is applied to solve over-determined polynomial systems by either finding a triangular representation of the solution set or by reducing the problem to eigenvalue computation. One of the ingredients of the subresultant method is the computation of a matrix that satisfies certain requirements, called the subresultant properties. Our general framework allows us to use matrices of significantly smaller size than previous methods. We prove that certain previously known matrix constructions, in particular, Macaulay's, Chardin's and Jouanolou's resultant and subresultant matrices possess the subresultant properties. However, these results rely on some assumptions about the regularity of the over-determined system to be solved. The appendix, written by Marc Chardin, contains relevant results on the regularity of n homogeneous forms in n variables.