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Creators/Authors contains: "Ayyildiz Akoglu, T"

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  1. ; (, Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989))
    Let 𝑓1,…,𝑓𝑚 be univariate polynomials with rational coefficients and I:=⟨𝑓1,…,𝑓𝑚⟩⊂ℚ[𝑥] be the ideal they generate. Assume that we are given approximations {𝑧1,…,𝑧𝑘}⊂ℚ[𝑖] for the common roots {𝜉1,…,𝜉𝑘}=𝑉(I)⊆ℂ . In this study, we describe a symbolic-numeric algorithm to construct a rational matrix, called Hermite matrix, from the approximate roots {𝑧1,…,𝑧𝑘} and certify that this matrix is the true Hermite matrix corresponding to the roots V(I) . Applications of Hermite matrices include counting and locating real roots of the polynomials and certifying their existence. 
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