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Class CrossRegion

A cross region is a distinction if 1) it is empty, 2) it is full, or 3) it is the rectangular cross of full regions and one distinction. Note that case 3 actually subsumes 1 and 2. Since the simple regions of a space are the intersections of a finite number of distinctions of a space, this implies that A cross region is simple if it is the rectangular cross of simple regions. In other words, a simple region is identical to the cross of its projections.

Package: Udanax-Gold
All Superclasses: Object Heaper XnRegion
Immediate Subclasses: GenericCrossRegion
Protocols: Object
Categories: Xanadu-Spaces-Cross

Class Methods

infostProtocol

Overrides: XnRegion class

Instance Methods

actualHashForEqual

To avoid overly burdensome canonicalization rules, my hash is calculated from the hash of my projections

Overrides: XnRegion
Overridden by: GenericCrossRegion

actualStepper: order

Overrides: XnRegion
Overridden by: GenericCrossRegion

asSimpleRegion

Overrides: XnRegion
Overridden by: GenericCrossRegion

boxes

Essential. Divide this Region up into a disjoint sequence of boxes. A box is a region which is the cross of its projections.

Overridden by: GenericCrossRegion

complement

Overrides: XnRegion
Overridden by: GenericCrossRegion

coordinateSpace

Overrides: XnRegion
Overridden by: GenericCrossRegion

count

Overrides: XnRegion
Overridden by: GenericCrossRegion

distinctions

Overrides: XnRegion
Overridden by: GenericCrossRegion

hasMember: atPos

Overrides: XnRegion
Overridden by: GenericCrossRegion

intersect: other

Overrides: XnRegion
Overridden by: GenericCrossRegion

isBox

Whether this Region is a box, ie. is equal to the cross of its projections.

Overridden by: GenericCrossRegion

isEmpty

Overrides: XnRegion
Overridden by: GenericCrossRegion

isEnumerable: order

Overrides: XnRegion
Overridden by: GenericCrossRegion

isEqual: other

Overrides: XnRegion
Overridden by: GenericCrossRegion

isFinite

Overrides: XnRegion
Overridden by: GenericCrossRegion

isSimple

Overrides: XnRegion
Overridden by: GenericCrossRegion

projection: index

The answer is the projection of this region into the specified dimension of the cross space

Overridden by: GenericCrossRegion

projections

Essential. The answer is the projection of this region into each dimension of the cross space. Note that two regions which are different can have the same projections.

Overridden by: GenericCrossRegion

simpleRegions: order

Overrides: XnRegion
Overridden by: GenericCrossRegion

simpleUnion: other

Overrides: XnRegion

unionWith: other

Overrides: XnRegion
Overridden by: GenericCrossRegion

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