A completion procedure for computing canonical basis for a k-Subalgebra
Proceedings of the third conference on Computers and mathematics
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
On the complexity of sparse elimination
Journal of Complexity
Analogs of Gro¨bner bases in polynomial rings over a ring
Journal of Symbolic Computation
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
SAGBI and SAGBI-Gröbner bases over principal ideal domains
Journal of Symbolic Computation
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Modern computer algebra
Gröbner bases, invariant theory and equivariant dynamics
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Parallel integer relation detection: techniques and applications
Mathematics of Computation
Applications of SAGBI-bases in dynamics
Journal of Symbolic Computation - Special issue: Algebra and computer analysis
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One way of solving polynomial systems of equations is by computing a Grobner basis, setting up an eigenvalue problem and then computing the eigenvalues numerically. This so-called eigenvalue method is an excellent bridge between symbolic and numeric computation, enabling the solution of larger systems than with purely symbolic methods. We investigate the case that the system of polynomial equations has symmetries. For systems with symmetry, some matrices in the eigenvalue method turn out to have special structure. The exploitation of this special structure is the aim of this paper. For theoretical development we make use of SAGBI bases of invariant rings. Examples from applications illustrate our new approach.