The complexity of robot motion planning
The complexity of robot motion planning
Using Symmetric Functions to Describe the Solution Set of a Zero Dimensional Ideal
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the complexity of Schmüdgen's positivstellensatz
Journal of Complexity
Bounding the radii of balls meeting every connected component of semi-algebraic sets
Journal of Symbolic Computation
Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems
ACM Transactions on Mathematical Software (TOMS)
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We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of R^k, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize @t of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex.