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FullRegion[n]

represents the full region .

Examples  
Basic Examples  
Scope  
Regions  
Properties & Relations  
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FullRegion

FullRegion[n]

represents the full region .

Examples

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Basic Examples  (2)

Region dimension:

Wolfram Language code: RegionDimension[FullRegion[7]]

Region membership condition:

Wolfram Language code: RegionMember[FullRegion[3], {x, y, z}]

Scope  (9)

Regions  (9)

Embedding dimension:

Wolfram Language code: RegionEmbeddingDimension[FullRegion[3]]

Geometric dimension:

Wolfram Language code: RegionDimension[FullRegion[3]]

Point membership test:

Wolfram Language code: RegionMember[FullRegion[4], {1, 2, 3, 4}]

Get conditions for point membership:

Wolfram Language code: RegionMember[FullRegion[4], {x, y, z, t}]

The measure of a FullRegion is infinite:

Wolfram Language code: RegionMeasure[FullRegion[3]]

And its centroid is indeterminate:

Wolfram Language code: RegionCentroid[FullRegion[3]]

Distance from a point:

Wolfram Language code: RegionDistance[FullRegion[2], {1, 1}]

Signed distance from a point:

Wolfram Language code: SignedRegionDistance[FullRegion[2], {1, 1}]

Nearest point in the region:

Wolfram Language code: RegionNearest[FullRegion[2], {1, 1}]

A full region is unbounded:

Wolfram Language code: BoundedRegionQ[FullRegion[3]]

And its range is necessarily infinite in all dimensions:

Wolfram Language code: RegionBounds[FullRegion[2]]

Integrate over a full region:

Wolfram Language code: Integrate[1 / (1 + x ^ 4 + y ^ 4 + z ^ 4), {x, y, z}∈FullRegion[3]]

Optimize over a full region:

Wolfram Language code: {MinValue[{x ^ 4 + y ^ 4 + z ^ 4 - x y z, {x, y, z}∈FullRegion[3]}, {x, y, z}], ArgMin[{x ^ 4 + y ^ 4 + z ^ 4 - x y z, {x, y, z}∈FullRegion[3]}, {x, y, z}]}

Solve equations in a full region:

Wolfram Language code: ℛ = FullRegion[3];
Wolfram Language code: Reduce[x^2 + y^2 + z^2 == 1 && {x, y, z}∈ℛ, {x, y, z}]

Properties & Relations  (3)

FullRegion is equivalent to an InfiniteLine in 1D:

Wolfram Language code: Subscript[ℛ, 1] = InfiniteLine[{0}, {1}]; Subscript[ℛ, 2] = FullRegion[1];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

FullRegion is equivalent to an InfinitePlane in 2D:

Wolfram Language code: Subscript[ℛ, 1] = InfinitePlane[{0, 0}, {{0, 1}, {1, 0}}]; Subscript[ℛ, 2] = FullRegion[2];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

FullRegion can be represented as a ConicHullRegion in any dimension:

Wolfram Language code: Subscript[ℛ, 1] = ConicHullRegion[{{0, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}]; Subscript[ℛ, 2] = FullRegion[4];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Research (2014), FullRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/FullRegion.html.

Text

Wolfram Research (2014), FullRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/FullRegion.html.

CMS

Wolfram Language. 2014. "FullRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FullRegion.html.

APA

Wolfram Language. (2014). FullRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FullRegion.html

BibTeX

@misc{reference.wolfram_2026_fullregion, author="Wolfram Research", title="{FullRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FullRegion.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_fullregion, organization={Wolfram Research}, title={FullRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/FullRegion.html}, note=[Accessed: 13-June-2026]}