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Name

hypersurface — A single normal hypersurface in a 4-manifold triangulation

Synopsis

Content Model 
hypersurface ::= (#PCDATA,
             compact?, realbdry?)
Attributes
NameTypeVersion
encNUMBER (required)Added in Regina 7.0
lenNUMBER (required) 
nameCDATA 

Description

A hypersurface element stores a single normal hypersurface in a 4-manifold triangulation.

A normal hypersurface in a P-pentachoron triangulation is traditionally represented by a vector of integers, whose length depends upon the specific vector encoding being used. For instance, a vector encoded in standard tetrahedron-prism coordinates will have length 15P, and a vector encoded in prism coordinates will have length 10P.

Warning

Since Regina 7.0, the specific vector encoding being used is now explicitly specified in the enc attribute. This might or might not be deducible from the coordinate system specified in the parent hypersurfaces. The parent list's coordinate system should only be used as a fallback if the enc attribute is not present.

The normal hypersurface vector is stored as the character data of this XML element as follows. Since a normal hypersurface vector will generally contain many zeroes, only the non-zero elements are listed. The character data should thus consist of a whitespace-separated sequence of integer pairs. Each integer pair represents a non-zero coordinate in the vector; the first element of the pair identifies which coordinate is being described (coordinates are numbered 0, 1, 2, ...) and the second element of the pair is the actual value at this coordinate.

Parents

The following elements contain hypersurface: hypersurfaces.

Children

The following elements occur in hypersurface: compact, realbdry.

Attributes

enc

The specific vector encoding used to represent this normal hypersurface. This will be given as an opaque integer; it is not meant to be interpreted manually, but instead should be passed to Regina's HyperEncoding::fromIntValue() function.

len

The length of the underlying normal hypersurface vector. This depends upon both the underlying triangulation and the specific vector encoding being used.

name

A human-readable name given to this hypersurface. Hypersurface names need not be distinct and exist merely for the convenience of the user.

Example

The following XML snippet represents a normal hypersurface in a 4-pentachoron triangulation. The normal hypersurface vector is: 

(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)

The child elements of this normal surface indicate that the surface is compact and has no real boundary. 

<hypersurface enc="287" len="60"> 10 1 25 1 36 1 51 1
    <realbdry value="F"/>
    <compact value="T"/> </hypersurface>
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