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Let V⊂ℝn, be a real algebraic variety, defined by a system of equations where.We denote by L the maximum of the bit lengths of descriptions of the coefficients of the system and we let. It is proved that for any com. ponent V of the variety V one can find a point, such that ¦x1¦<2H(r,L) (i=1,..., n, where H is some polynomial, independent of the original system. If V is compact, then any pointx ε V has the property indicated.

Estimates of real roots of a system of algebraic equations