BUILT-IN MATHEMATICA SYMBOL

SemialgebraicComponentInstances

gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs in the variables

,

, ....

Any solution to the set of inequalities can be connected by a continuous path to one of the points returned by SemialgebraicComponentInstances.

SemialgebraicComponentInstances produces a list of rules for variables, of the same type as Solve.

Find at least one sample point in each distinct component:

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A univariate polynomial inequality:

Multivariate polynomial equations and inequalities:

Boolean combinations of equations and inequalities:

Find at least one point in each interval defined by a univariate polynomial inequality:

With a weak inequality you also get the roots:

Find at least one point in each connected component of a two-dimensional planar set:

Find at least one point in each connected component of a surface:

Find at least one point in each connected component of a solid:

The points satisfy the inequalities:

Use the points to check whether a numerically obtained graphic is missing parts of the set:

The returned instances satisfy the input inequalities:

Use FindInstance to find a single instance satisfying the inequalities:

Use CylindricalDecomposition or Reduce to get a full description of the solution set:

An empty list is returned if the inequalities have no solutions:

An equivalent result can be obtained using Resolve: