We prove Khovanskii’s theorem  which gives an upper bound on the number of non-degenerate real solutions of a system of n polynomial equations in n variables which depends only on n and the number of distinct terms occurring in the polynomials. This result is in fact a consequence of a more general result dealing with certain systems of transcendental equations. A variant of Rolle’s theorem and Bézout’s inequality enter in the proof. As a consequence we deduce Grigoriev’s and Risler’s lower bound [209, 438] on the additive complexity of a univariate real polynomial in terms of the number of its real roots.
KeywordsReal Root Regular Point Additive Complexity Univariate Polynomial Positive Real Root
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