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.

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Here is a point from each of the three intervals forming the set of solutions of .

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This gives one point in each of the two connected components of the set bounded by the circle and the hyperbola .

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This proves that the ball is contained in the ellipsoid .

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