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Creators/Authors contains: "Ayyildiz Akoglu, Tulay"

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  1. ; (, Journal of Symbolic Computation)
    Let I = f1,..., fm ⊂ Q[x1,..., xn] be a zero dimensional radical ideal defined by polynomials given with exact rational coefficients. Assume that we are given approximations {z1,..., zk} ⊂ Cn for the common roots {ξ1,..., ξk} = V (I) ⊆ Cn. In this paper we show how to construct and certify the rational entries of Hermite matrices for I from the approximate roots {z1,..., zk}. When I is non-radical, we give methods to construct and certify Hermite matrices for √ I from the approximate roots. Furthermore, we use signatures of these Hermite matrices to give rational certificates of non-negativity of a given polynomial over a (possibly positive dimensional) real variety, as well as certificates that there is a real root within an ε distance from a given point z ∈ Qn. 
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