SemialgebraicComponentInstances

SemialgebraicComponentInstances[ineqs,{x1,x2,…}]

gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs in the variables x1, x2, ….

Details

Examples

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Basic Examples  (1)

Find at least one sample point in each distinct component:

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:

Properties & Relations  (2)

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:

Wolfram Research (2007), SemialgebraicComponentInstances, Wolfram Language function, https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html.

Text

Wolfram Research (2007), SemialgebraicComponentInstances, Wolfram Language function, https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html.

CMS

Wolfram Language. 2007. "SemialgebraicComponentInstances." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html.

APA

Wolfram Language. (2007). SemialgebraicComponentInstances. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html

BibTeX

@misc{reference.wolfram_2024_semialgebraiccomponentinstances, author="Wolfram Research", title="{SemialgebraicComponentInstances}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_semialgebraiccomponentinstances, organization={Wolfram Research}, title={SemialgebraicComponentInstances}, year={2007}, url={https://reference.wolfram.com/language/ref/SemialgebraicComponentInstances.html}, note=[Accessed: 21-December-2024 ]}