An algorithm reduces finding parameter conditions for specific eigenvalue configurations of two parametric symmetric matrices to real root counting of symmetric polynomials via the Fundamental Theorem of Symmetric Polynomials and Descartes' rule of signs.
Hong.Improvements in CAD–based Quantifier Elimination
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Conditions for eigenvalue configurations of two real symmetric matrices (symmetric polynomial approach)
An algorithm reduces finding parameter conditions for specific eigenvalue configurations of two parametric symmetric matrices to real root counting of symmetric polynomials via the Fundamental Theorem of Symmetric Polynomials and Descartes' rule of signs.