Solving Systems of Strict Polynomial Inequalities

extensions of some polynomial inequalities to the polar derivative

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Solving Systems of Polynomial

Current geometric and solid modeling systems use semi-algebraic sets for deening the boundaries of solid objects, curves and surfaces, geometric constraints with mating relationship in a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many of the geometric operations on the solid boundaries or interacting with geometric constraints is re...

On linear systems containing strict inequalities

This paper deals with systems of an arbitrary (possibly infinite) number of both weak and strict linear inequalities. We analize the existence of solutions for such kind of systems and show that the large class of convex sets which admit this kind of linear representations (i.e., the so-called evenly convex sets) enjoys most of the well-known properties of the subclass of the closed convex sets...

Solving parametric polynomial systems

We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like C = {x ∈ C, p1(x) = 0, , ps(x) = 0, f1(x) 0, , fl(x) 0} or S = {x ∈ R, p1(x) = 0, , ps(x) = 0, f1(x)> 0, , fl(x)> 0}, where pi, fi ∈Q[U , X], U = [U1, , Ud] is the set of parameters and X = [Xd+1, , Xn] the set of unknowns. If ΠU denotes the canonical projection onto the parameter’s space, solvi...

Solving Systems of Polynomial Equations