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We show that detecting real roots for honestly <i>n</i>-variate (<i>n</i>+2)-nomials with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any fixed n<i>n</i>. The best previous complexity bounds were exponential in the sparse encoding, even for <i>n</i> fixed. We then give a characterization of those functions… (More)

- Frederic Bihan, J. Maurice Rojas, Casey E. Stella
- 2004

Let FEAS R denote the problem of deciding whether a given system of real polynomial equations has a real root or not. We give a new, nearly tight threshold for when m is large enough to make FEAS R be NP-hard for input a single n-variate polynomial with exactly m monomial terms. We also outline a connection between the complexity of FEAS R , the topology of… (More)

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