Regina Calculation Engine
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Stores the vector of a single normal hypersurface in a 4-manifold triangulation.
More...
#include <hypersurface/normalhypersurface.h>
Public Member Functions | |
NormalHypersurfaceVector (size_t length) | |
Creates a new vector all of whose entries are initialised to zero. More... | |
NormalHypersurfaceVector (const Vector< LargeInteger > &cloneMe) | |
Creates a new vector that is a clone of the given vector. More... | |
virtual | ~NormalHypersurfaceVector () |
A virtual destructor. More... | |
const Ray & | coords () const |
Gives read-only access to the underlying vector of coordinates. More... | |
virtual NormalHypersurfaceVector * | clone () const =0 |
Creates a newly allocated clone of this vector. More... | |
size_t | size () const |
Returns the number of coordinates in the underlying vector. More... | |
const LargeInteger & | operator[] (size_t index) const |
Returns the given coordinate from the underlying vector. More... | |
virtual void | setElement (size_t index, const LargeInteger &value) |
Sets the given normal coordinate to the given value. More... | |
virtual void | operator+= (const NormalHypersurfaceVector &other) |
Adds the given vector to this vector. More... | |
virtual void | scaleDown () |
Scales this vector down by the greatest common divisor of all its elements. More... | |
virtual bool | isCompact (const Triangulation< 4 > *triang) const |
Determines if the normal hypersurface represented is compact (has finitely many pieces). More... | |
virtual bool | isVertexLinking (const Triangulation< 4 > *triang) const |
Determines if the normal hypersurface represented is vertex linking. More... | |
virtual const Vertex< 4 > * | isVertexLink (const Triangulation< 4 > *triang) const |
Determines if a rational multiple of the normal hypersurface represented is the link of a single vertex. More... | |
virtual const Edge< 4 > * | isThinEdgeLink (const Triangulation< 4 > *triang) const |
Determines if a rational multiple of the normal hypersurface represented is the thin link of a single edge. More... | |
virtual LargeInteger | tetrahedra (size_t pentIndex, int vertex, const Triangulation< 4 > *triang) const =0 |
Returns the number of tetrahedron pieces of the given type in this normal hypersurface. More... | |
virtual LargeInteger | prisms (size_t pentIndex, int prismType, const Triangulation< 4 > *triang) const =0 |
Returns the number of prism pieces of the given type in this normal hypersurface. More... | |
virtual LargeInteger | edgeWeight (size_t edgeIndex, const Triangulation< 4 > *triang) const =0 |
Returns the number of times this normal hypersurface crosses the given edge. More... | |
NormalHypersurfaceVector & | operator= (const NormalHypersurfaceVector &)=delete |
Static Public Member Functions | |
static NormalHypersurfaceVector * | makeZeroVector (const Triangulation< 4 > *triangulation) |
Returns a new normal hypersurface vector of the appropriate length for the given triangulation and for the coordinate system corresponding to this subclass of NormalHypersurfaceVector. More... | |
static MatrixInt * | makeMatchingEquations (const Triangulation< 4 > *triangulation) |
Creates a new set of normal hypersurface matching equations for the given triangulation using the coordinate system corresponding to this particular subclass of NormalHypersurfaceVector. More... | |
static EnumConstraints * | makeEmbeddedConstraints (const Triangulation< 4 > *triangulation) |
Creates a new set of validity constraints representing the condition that normal hypersurfaces be embedded. More... | |
Protected Attributes | |
Ray | coords_ |
The raw vector of normal coordinates. More... | |
Stores the vector of a single normal hypersurface in a 4-manifold triangulation.
The different subclasses of NormalHypersurfaceVector use different underlying coordinate systems for the normal solution space. However, the various coordinate retrieval routines will return values that are independent of the underlying coordinate system. Thus the coordinates of the normal hypersurface in any coordinate system can be determined without knowledge of the specific underlying coordinate system being used.
Note that non-compact hypersurfaces (surfaces with infinitely many pieces) are allowed; in these cases, the corresponding coordinate lookup routines should return LargeInteger::infinity where appropriate.
All subclasses of NormalHypersurfaceVector must have the following properties:
When deriving classes from NormalHypersurfaceVector:
class(size_t length)
and class(const Vector<LargeInteger>& cloneMe)
must be declared and implemented; these will usually just call the corresponding superclass constructors. void makeZeroVector(const Triangulation<4>*)
, MatrixInt* makeMatchingEquations(const Triangulation<4>*)
and makeEmbeddedConstraints(const Triangulation<4>*) must be declared and implemented.
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inline |
Creates a new vector all of whose entries are initialised to zero.
length | the number of elements in the new vector. |
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inline |
Creates a new vector that is a clone of the given vector.
cloneMe | the vector to clone. |
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inlinevirtual |
A virtual destructor.
This is required because here we introduce virtual functions into the Ray hierarchy.
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pure virtual |
Creates a newly allocated clone of this vector.
The clone will be of the same subclass of NormalHypersurfaceVector as this vector.
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inline |
Gives read-only access to the underlying vector of coordinates.
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pure virtual |
Returns the number of times this normal hypersurface crosses the given edge.
See NormalHypersurface::edgeWeight() for further details.
edgeIndex | the index in the triangulation of the edge in which we are interested; this should be between 0 and Triangulation<4>::countEdges()-1 inclusive. |
triang | the triangulation in which this normal hypersurface lives. |
Implemented in regina::HSVectorStandard.
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virtual |
Determines if the normal hypersurface represented is compact (has finitely many pieces).
The default implementation for this routine simply runs through every piece type until a piece type with infinite piece count is found or all piece types have been examined. Subclasses of NormalHypersurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal hypersurface lives. |
true
if and only if the normal hypersurface represented is compact.
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virtual |
Determines if a rational multiple of the normal hypersurface represented is the thin link of a single edge.
The default implementation for this routine involves counting the number of pieces of every type. Subclasses of NormalHypersurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal hypersurface lives. |
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virtual |
Determines if a rational multiple of the normal hypersurface represented is the link of a single vertex.
The default implementation for this routine involves counting the number of pieces of every type. Subclasses of NormalSurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal hypersurface lives. |
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virtual |
Determines if the normal hypersurface represented is vertex linking.
A vertex linking hypersurface contains only tetrahedra.
The default implementation for this routine simply runs through every non-tetrahedron piece type ensuring that each has no corresponding pieces. Subclasses of NormalHypersurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal hypersurface lives. |
true
if and only if the normal hypersurface represented is vertex linking.
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static |
Creates a new set of validity constraints representing the condition that normal hypersurfaces be embedded.
The validity constraints will be expressed relative to the coordinate system corresponding to this particular subclass of NormalHypersurfaceVector.
triangulation | the triangulation upon which these validity constraints will be based. |
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static |
Creates a new set of normal hypersurface matching equations for the given triangulation using the coordinate system corresponding to this particular subclass of NormalHypersurfaceVector.
See makeMatchingEquations() for further details.
triangulation | the triangulation upon which these matching equations will be based. |
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static |
Returns a new normal hypersurface vector of the appropriate length for the given triangulation and for the coordinate system corresponding to this subclass of NormalHypersurfaceVector.
All elements of the new vector will be initialised to zero.
See makeZeroVector() for further details.
triangulation | the triangulation upon which the underlying coordinate system is based. |
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inlinevirtual |
Adds the given vector to this vector.
This behaves correctly in the case where other is this
.
The default implementation simply adds the coordinates of the underlying vectors. Subclasses should reimplement this if they carry any additional information that also need adjusting.
other | the vector to add to this vector. |
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inline |
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pure virtual |
Returns the number of prism pieces of the given type in this normal hypersurface.
See NormalHypersurface::prisms() for further details.
pentIndex | the index in the triangulation of the pentachoron in which the requested prism pieces reside; this should be between 0 and Triangulation<4>::size()-1 inclusive. |
prismType | specifies the edge of the given pentachoron that this prism separates from the opposite triangle; this should be between 0 and 9 inclusive. |
triang | the triangulation in which this normal hypersurface lives. |
Implemented in regina::HSVectorStandard.
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inlinevirtual |
Scales this vector down by the greatest common divisor of all its elements.
The resulting vector will be the smallest multiple of the original that maintains integral entries, and these entries will have the same signs as the originals.
This routine poses no problem for vectors containing infinite elements; such elements are simply ignored and left at infinity.
The default implementation simply scales down the underlying vector. Subclasses should reimplement this if they carry any additional information that also needs adjusting.
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inlinevirtual |
Sets the given normal coordinate to the given value.
The default implementation simply sets the coordinate in the underlying vector. Subclasses should reimplement this if they carry any additional information that also need adjusting.
index | the index of the coordinate to set; this must e between 0 and size()-1 inclusive. |
value | the new value to assign to the given coordinate. |
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inline |
Returns the number of coordinates in the underlying vector.
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pure virtual |
Returns the number of tetrahedron pieces of the given type in this normal hypersurface.
See NormalHypersurface::tetrahedra() for further details.
pentIndex | the index in the triangulation of the pentachoron in which the requested tetrahedron pieces reside; this should be between 0 and Triangulation<4>::size()-1 inclusive. |
vertex | the vertex of the given pentachoron around which the requested tetrahedron pieces lie; this should be between 0 and 4 inclusive. |
triang | the triangulation in which this normal hypersurface lives. |
Implemented in regina::HSVectorStandard.
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protected |
The raw vector of normal coordinates.