This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# SemialgebraicComponentInstances

 SemialgebraicComponentInstancesgives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs in the variables , , ....
• Lists or logical combinations of inequalities can be given.
Find at least one sample point in each distinct component:
Find at least one sample point in each distinct component:
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 Scope   (3)
A univariate polynomial inequality:
Multivariate polynomial equations and inequalities:
Boolean combinations of equations and inequalities:
 Applications   (4)
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:
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