This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 Algebra`AlgebraicInequalities` The package provides a function for solving systems of strong polynomial inequalities in one or more unknowns. To be precise, SemialgebraicComponents[ineqs, vars] gives a finite set of solutions of the system of inequalities. That is, within the set of solutions, any solution can be connected by a continuous path to a solution in the finite set. The variable ineqs is a list of strong inequalities, where both sides of each inequality are polynomials in variables vars with rational coefficients. In other words, SemialgebraicComponents[ineqs, vars] gives at least one point in each connected component of the open semialgebraic set defined by inequalities ineqs. Solutions of inequalities. This loads the package. In[1]:= < 0}, x] Out[2]= This gives one point in each of the two connected components of the set bounded by the circle and the hyperbola . In[3]:= SemialgebraicComponents[{x^2 + y^2 < 4, x y > 1}, {x, y}] Out[3]= This proves that the ball is contained in the ellipsoid . In[4]:= SemialgebraicComponents[{x^2 + y^2/4 + z^2/9 > 1, x^2 + (y - 1)^2 + (z - 2)^2 < 1/9}, {x, y, z}] Out[4]=