Solutions of systems of algebraic equations and linear maps on residue class rings
Journal of Symbolic Computation
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
Analysis of zero clusters in multivariate polynomial systems
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Gröbner bases and matrix eigenproblems
ACM SIGSAM Bulletin
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 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
Systems of Algebraic Equations Solved by Means of Endomorphisms
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the complexity of computing grobner bases for zero-dimensional polynomial ideals
On the complexity of computing grobner bases for zero-dimensional polynomial ideals
Border bases of positive dimensional polynomial ideals
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing the multiplicity structure from geometric involutive form
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Irreducible decomposition of polynomial ideals
Journal of Symbolic Computation
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The solutions of a polynomial system can be computed using eigenvalues and eigenvectors of certain endomorphisms. There are two different approaches, one by using the (right) eigenvectors of the representation matrices, one by using the (right) eigenvectors of their transposed ones, i.e. their left eigenvectors. For both approaches, we describe the common eigenspaces and give an algorithm for computing the solution of the algebraic system. As a byproduct, we present a new method for computing radicals of zero-dimensional ideals. Copyright 2001 Academic Press.