Regina Calculation Engine
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regina::NHomologicalData Class Reference

Data type that deals with all the detailed homological information in a manifold. More...

#include <triangulation/nhomologicaldata.h>

Inheritance diagram for regina::NHomologicalData:
regina::ShortOutput< NHomologicalData > regina::Output< NHomologicalData, false >

Public Member Functions

 NHomologicalData (const NTriangulation &input)
 Takes as input a triangulation. More...
 
 NHomologicalData (const NHomologicalData &h)
 Copy constructor. More...
 
 ~NHomologicalData ()
 Destructor. More...
 
void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object to the given output stream. More...
 
const NMarkedAbelianGrouphomology (unsigned q)
 This routine gives access to the manifold's homology computed with the regular CW-decomposition. More...
 
REGINA_DEPRECATED const NMarkedAbelianGroupgetHomology (unsigned q)
 Deprecated routine that gives access to the manifold's homology computed with the regular CW-decomposition. More...
 
const NMarkedAbelianGroupbdryHomology (unsigned q)
 This routine gives access to the homology of the boundary of the manifold, computed with the regular CW-decomposition. More...
 
REGINA_DEPRECATED const NMarkedAbelianGroupgetBdryHomology (unsigned q)
 Deprecated routine that gives access to the homology of the boundary of the manifold, computed with the regular CW-decomposition. More...
 
const NHomMarkedAbelianGroupbdryHomologyMap (unsigned q)
 This routine gives access to the homomorphism from the homology of the boundary to the homology of the manifold. More...
 
REGINA_DEPRECATED const NHomMarkedAbelianGroupgetBdryHomologyMap (unsigned q)
 Deprecated routine that gives access to the homomorphism from the homology of the boundary to the homology of the manifold. More...
 
const NMarkedAbelianGroupdualHomology (unsigned q)
 This routine gives access to the manifold's homology computed with the dual CW-decomposition. More...
 
REGINA_DEPRECATED const NMarkedAbelianGroupgetDualHomology (unsigned q)
 Deprecated routine that gives access to the manifold's homology computed with the dual CW-decomposition. More...
 
const NHomMarkedAbelianGrouph1CellAp ()
 Returns the isomorphism from dualHomology(1) to homology(1) given by a cellular approximation to the identity map on the manifold. More...
 
REGINA_DEPRECATED const NHomMarkedAbelianGroupgetH1CellAp ()
 Deprecated routine that returns the isomorphism from dualHomology(1) to homology(1) given by a cellular approximation to the identity map on the manifold. More...
 
unsigned long countStandardCells (unsigned dimension)
 Returns the number of cells of the given dimension in the standard genuine CW-decomposition of the manifold. More...
 
REGINA_DEPRECATED unsigned long getNumStandardCells (unsigned dimension)
 Deprecated routine that returns the number of cells of the given dimension in the standard genuine CW-decomposition of the manifold. More...
 
unsigned long countDualCells (unsigned dimension)
 Returns the number of cells of the given dimension in the dual CW-decomposition of the manifold. More...
 
REGINA_DEPRECATED unsigned long getNumDualCells (unsigned dimension)
 Deprecated routine that returns the number of cells of the given dimension in the dual CW-decomposition of the manifold. More...
 
unsigned long countBdryCells (unsigned dimension)
 Returns the number of cells of the given dimension in the standard CW-decomposition of the boundary of the manifold. More...
 
REGINA_DEPRECATED unsigned long getNumBdryCells (unsigned dimension)
 Deprecated routine that returns the number of cells of the given dimension in the standard CW-decomposition of the boundary of the manifold. More...
 
long eulerChar ()
 The proper Euler characteristic of the manifold, computed from the dual CW-decomposition. More...
 
REGINA_DEPRECATED long getEulerChar ()
 Deprecated routine that returns the proper Euler characteristic of the manifold, computed from the CW-decomposition. More...
 
const std::vector< std::pair< NLargeInteger, std::vector< unsigned long > > > & torsionRankVector ()
 Returns the torsion form rank vector. More...
 
REGINA_DEPRECATED const std::vector< std::pair< NLargeInteger, std::vector< unsigned long > > > & getTorsionRankVector ()
 Deprecated routine that returns the torsion form rank vector. More...
 
const std::string & torsionRankVectorString ()
 Same as torsionRankVector() but returns as a human-readable string. More...
 
REGINA_DEPRECATED const std::string & getTorsionRankVectorString ()
 Deprecated routine that returns torsionRankVector() as a human-readable string. More...
 
const std::vector< NLargeInteger > & torsionSigmaVector ()
 Returns the 2-torsion sigma vector. More...
 
REGINA_DEPRECATED const std::vector< NLargeInteger > & getTorsionSigmaVector ()
 Deprecated routine that returns the 2-torsion sigma vector. More...
 
const std::string & torsionSigmaVectorString ()
 Same as torsionSigmaVector() but returns as a human-readable string. More...
 
REGINA_DEPRECATED const std::string & getTorsionSigmaVectorString ()
 Deprecated routine that returns torsionSigmaVector() as a human-readable string. More...
 
const std::vector< std::pair< NLargeInteger, std::vector< int > > > & torsionLegendreSymbolVector ()
 Returns the odd p-torsion Legendre symbol vector. More...
 
REGINA_DEPRECATED const std::vector< std::pair< NLargeInteger, std::vector< int > > > & getTorsionLegendreSymbolVector ()
 Deprecated routine that returns the odd p-torsion Legendre symbol vector. More...
 
const std::string & torsionLegendreSymbolVectorString ()
 Same as torsionLegendreSymbolVector() but returns as a human-readable string. More...
 
REGINA_DEPRECATED const std::string & getTorsionLegendreSymbolVectorString ()
 Deprecated routine that returns torsionLegendreSymbolVector() as a human-readable string. More...
 
bool formIsHyperbolic ()
 Returns true iff torsion linking form is `hyperbolic' in the linking-form sense of the word. More...
 
bool formIsSplit ()
 Returns true iff the torsion linking form is split. More...
 
bool formSatKK ()
 Returns true iff the torsion linking form satisfies the Kawauchi-Kojima 2-torsion condition. More...
 
const std::string & embeddabilityComment ()
 Returns a comment on whether the manifold might embed in a homology 3-sphere or 4-sphere. More...
 
REGINA_DEPRECATED const std::string & getEmbeddabilityComment ()
 Deprecated routine that returns a comment on whether the manifold might embed in a homology 3-sphere or 4-sphere. More...
 
void writeTextLong (std::ostream &out) const
 A default implementation for detailed output. More...
 
std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 
REGINA_DEPRECATED std::string toString () const
 A deprecated alias for str(). More...
 
REGINA_DEPRECATED std::string toStringLong () const
 A deprecated alias for detail(). More...
 

Detailed Description

Data type that deals with all the detailed homological information in a manifold.

This information includes:

This class takes a "least effort" approach to all computations. It only computes what is neccessary for your requests. It also keeps a record of all previous computations you've made. If a computation can be sped up by not recomputing some data, it takes that short-cut.

All these algorithms use two transverse CW decompositions of the manifold. They correspond to the (possibly ideal) triangulation native to Regina, and the dual polyhedral (CW) decomposition which appears in Seifert and Threlfall's textbook.

In the following lists we describe the canonical ordering of both the cells and the dual cells of the given triangulation.

First we list the cell orderings for the standard CW decomposition, which most closely resembles the ideal triangulation.

Next we list the cell orderings for the dual CW decomposition: if the standard CW decomposition came from a morse function f, this would be the one for -f.

This class will eventually be removed in a future release of Regina. A new and more flexible class called NCellularData will take its place.

Author
Ryan Budney

Constructor & Destructor Documentation

§ NHomologicalData() [1/2]

regina::NHomologicalData::NHomologicalData ( const NTriangulation input)
inline

Takes as input a triangulation.

This class takes its own copy of the input triangulation. This means that the input triangulation can change or even be destroyed, and this homological data will happily continue to work with the original triangulation as it was first passed to the constructor.

Parameters
inputthe triangulation to use.

§ NHomologicalData() [2/2]

regina::NHomologicalData::NHomologicalData ( const NHomologicalData h)
inline

Copy constructor.

Parameters
hthe homological data to clone.

§ ~NHomologicalData()

regina::NHomologicalData::~NHomologicalData ( )
inline

Destructor.

Member Function Documentation

§ bdryHomology()

const NMarkedAbelianGroup& regina::NHomologicalData::bdryHomology ( unsigned  q)

This routine gives access to the homology of the boundary of the manifold, computed with the regular CW-decomposition.

Parameters
qthe dimension of the homology group: can be 0, 1 or 2.
Returns
the q-th boundary homology group, in standard cellular homology coordinates

§ bdryHomologyMap()

const NHomMarkedAbelianGroup& regina::NHomologicalData::bdryHomologyMap ( unsigned  q)

This routine gives access to the homomorphism from the homology of the boundary to the homology of the manifold.

Parameters
qthe dimension of the map: can be 0, 1 or 2.
Returns
the map from H_q of the boundary to H_q of the manifold, computed in standard coordinates.

§ countBdryCells()

unsigned long regina::NHomologicalData::countBdryCells ( unsigned  dimension)
inline

Returns the number of cells of the given dimension in the standard CW-decomposition of the boundary of the manifold.

This is a subcomplex of the complex used in countStandardCells().

Parameters
dimensionthe dimension of the cells in question; this must be 0, 1 or 2.
Returns
the number of cells of the given dimension in the standard CW-decomposition of the boundary.

§ countDualCells()

unsigned long regina::NHomologicalData::countDualCells ( unsigned  dimension)
inline

Returns the number of cells of the given dimension in the dual CW-decomposition of the manifold.

This is typically much smaller than countStandardCells().

Parameters
dimensionthe dimension of the cells in question; this must be 0, 1, 2 or 3.
Returns
the number of cells of the given dimension in the dual CW-decomposition to the triangulation.

§ countStandardCells()

unsigned long regina::NHomologicalData::countStandardCells ( unsigned  dimension)
inline

Returns the number of cells of the given dimension in the standard genuine CW-decomposition of the manifold.

In the case that the triangulation is a proper triangulation of a manifold (or delta-complex decomposition) it simply returns the same information as in the NTriangulation vertex, edge, face and tetrahedron lists.

In the case that this is an ideal triangulation, this algorithm returns the details of the corresponding compact manifold with boundary a union of closed surfaces.

Parameters
dimensionthe dimension of the cells in question; this must be 0, 1, 2 or 3.
Returns
the number of cells of the given dimension in the standard CW-decomposition of the closed manifold.

§ detail()

std::string regina::Output< NHomologicalData , supportsUtf8 >::detail ( ) const
inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns
a detailed text representation of this object.

§ dualHomology()

const NMarkedAbelianGroup& regina::NHomologicalData::dualHomology ( unsigned  q)

This routine gives access to the manifold's homology computed with the dual CW-decomposition.

This routine is typically faster than homology() since the dual CW-decomposition generally has far fewer cells.

Note that the groups returned by homology() and dualHomology() are isomorphic, though they are generally described by different presentations.

Parameters
qthe dimension of the homology group: can be 0, 1, 2 or 3.
Returns
the q-th homology group, computed in the dual CW-decomposition.

§ embeddabilityComment()

const std::string & regina::NHomologicalData::embeddabilityComment ( )
inline

Returns a comment on whether the manifold might embed in a homology 3-sphere or 4-sphere.

Basically, this routine runs through all the Kawauchi-Kojima conditions, plus a few other `elementary' conditions.

Each comment will be formatted as one or more English sentences (i.e., with capitalisation and punctuation). The comments themselves are subject to change between releases of Regina, since later releases may have more detailed tests at their disposal.

This routine is available for both orientable and non-orientable triangulations. In the non-orientable case it may return additional information regarding the orientable double cover.

Precondition
The triangulation is of a connected 3-manifold.
Returns
a string giving a one-line description of what is known about where this manifold embeds, based solely on the manifold's homological data.

§ eulerChar()

long int regina::NHomologicalData::eulerChar ( )
inline

The proper Euler characteristic of the manifold, computed from the dual CW-decomposition.

This routine calculates the Euler characteristic of the corresponding compact triangulated 3-manifold, with each ideal vertex treated as a surface boundary component.

This routine returns the same value as NTriangulation::eulerCharManifold(), though it computes it in a different way.

On the other hand, this routine differs from NTriangulation::eulerCharTri(), which handles ideal triangulations in a non-standard way (treating each ideal vertex as just a single vertex).

Returns
the Euler characteristic of the corresponding compact triangulated 3-manifold.

§ formIsHyperbolic()

bool regina::NHomologicalData::formIsHyperbolic ( )

Returns true iff torsion linking form is `hyperbolic' in the linking-form sense of the word.

To be a little more precise, Poincare-duality in a compact orientable boundaryless manifold gives an isomorphism between the torsion subgroup of H_1(M) denoted tH_1(M) and Hom(tH_1(M),Q/Z), where Q is the rationals and Z the integers. The associated bilinear form (with values in Q/Z) is said to be `hyperbolic' if tH_1(M) splits as a direct sum A+B such that Poincare duality sends A to Hom(B,Q/Z) and B to Hom(A,Q/Z).

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
true iff the torsion linking form is hyperbolic.

§ formIsSplit()

bool regina::NHomologicalData::formIsSplit ( )
inline

Returns true iff the torsion linking form is split.

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
true iff the linking form is split.

§ formSatKK()

bool regina::NHomologicalData::formSatKK ( )
inline

Returns true iff the torsion linking form satisfies the Kawauchi-Kojima 2-torsion condition.

This condition states that on all elements x of order 2^k, 2^{k-1}form(x,x) = 0.

This is a neccessary condition for an orientable 3-manifold perhaps with boundary to embed in a homology 4-sphere.

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
true iff the form satisfies the 2-torsion condition of Kawauchi-Kojima.

§ getBdryHomology()

const NMarkedAbelianGroup & regina::NHomologicalData::getBdryHomology ( unsigned  q)
inline

Deprecated routine that gives access to the homology of the boundary of the manifold, computed with the regular CW-decomposition.

Deprecated:
This routine has been renamed to bdryHomology(). See the bdryHomology() documentation for further details.

§ getBdryHomologyMap()

const NHomMarkedAbelianGroup & regina::NHomologicalData::getBdryHomologyMap ( unsigned  q)
inline

Deprecated routine that gives access to the homomorphism from the homology of the boundary to the homology of the manifold.

Deprecated:
This routine has been renamed to bdryHomologyMap(). See the bdryHomologyMap() documentation for further details.

§ getDualHomology()

const NMarkedAbelianGroup & regina::NHomologicalData::getDualHomology ( unsigned  q)
inline

Deprecated routine that gives access to the manifold's homology computed with the dual CW-decomposition.

Deprecated:
This routine has been renamed to dualHomology(). See the dualHomology() documentation for further details.

§ getEmbeddabilityComment()

const std::string & regina::NHomologicalData::getEmbeddabilityComment ( )
inline

Deprecated routine that returns a comment on whether the manifold might embed in a homology 3-sphere or 4-sphere.

Deprecated:
This routine has been renamed to embeddabilityComment(). See the embeddabilityComment() documentation for further details.

§ getEulerChar()

long int regina::NHomologicalData::getEulerChar ( )
inline

Deprecated routine that returns the proper Euler characteristic of the manifold, computed from the CW-decomposition.

Deprecated:
This routine has been renamed to eulerChar(). See the eulerChar() documentation for further details.

§ getH1CellAp()

const NHomMarkedAbelianGroup & regina::NHomologicalData::getH1CellAp ( )
inline

Deprecated routine that returns the isomorphism from dualHomology(1) to homology(1) given by a cellular approximation to the identity map on the manifold.

Deprecated:
This routine has been renamed to h1CellAp(). See the h1CellAp() documentation for further details.

§ getHomology()

const NMarkedAbelianGroup & regina::NHomologicalData::getHomology ( unsigned  q)
inline

Deprecated routine that gives access to the manifold's homology computed with the regular CW-decomposition.

Deprecated:
This routine has been renamed to homology(). See the homology() documentation for further details.

§ getNumBdryCells()

unsigned long regina::NHomologicalData::getNumBdryCells ( unsigned  dimension)
inline

Deprecated routine that returns the number of cells of the given dimension in the standard CW-decomposition of the boundary of the manifold.

Deprecated:
This routine has been renamed to countBdryCells(). See the countBdryCells() documentation for further details.

§ getNumDualCells()

unsigned long regina::NHomologicalData::getNumDualCells ( unsigned  dimension)
inline

Deprecated routine that returns the number of cells of the given dimension in the dual CW-decomposition of the manifold.

Deprecated:
This routine has been renamed to countDualCells(). See the countDualCells() documentation for further details.

§ getNumStandardCells()

unsigned long regina::NHomologicalData::getNumStandardCells ( unsigned  dimension)
inline

Deprecated routine that returns the number of cells of the given dimension in the standard genuine CW-decomposition of the manifold.

Deprecated:
This routine has been renamed to countStandardCells(). See the countStandardCells() documentation for further details.

§ getTorsionLegendreSymbolVector()

const std::vector< std::pair< NLargeInteger, std::vector< int > > > & regina::NHomologicalData::getTorsionLegendreSymbolVector ( )
inline

Deprecated routine that returns the odd p-torsion Legendre symbol vector.

Deprecated:
This routine has been renamed to torsionLegendreSymbolVector(). See the torsionLegendreSymbolVector() documentation for further details.

§ getTorsionLegendreSymbolVectorString()

const std::string & regina::NHomologicalData::getTorsionLegendreSymbolVectorString ( )
inline

Deprecated routine that returns torsionLegendreSymbolVector() as a human-readable string.

Deprecated:
This routine has been renamed to torsionLegendreSymbolVectorString(). See the torsionLegendreSymbolVectorString() documentation for further details.

§ getTorsionRankVector()

const std::vector< std::pair< NLargeInteger, std::vector< unsigned long > > > & regina::NHomologicalData::getTorsionRankVector ( )
inline

Deprecated routine that returns the torsion form rank vector.

Deprecated:
This routine has been renamed to torsionRankVector(). See the torsionRankVector() documentation for further details.

§ getTorsionRankVectorString()

const std::string & regina::NHomologicalData::getTorsionRankVectorString ( )
inline

Deprecated routine that returns torsionRankVector() as a human-readable string.

Deprecated:
This routine has been renamed to torsionRankVectorString(). See the torsionRankVectorString() documentation for further details.

§ getTorsionSigmaVector()

const std::vector< NLargeInteger > & regina::NHomologicalData::getTorsionSigmaVector ( )
inline

Deprecated routine that returns the 2-torsion sigma vector.

Deprecated:
This routine has been renamed to torsionSigmaVector(). See the torsionSigmaVector() documentation for further details.

§ getTorsionSigmaVectorString()

const std::string & regina::NHomologicalData::getTorsionSigmaVectorString ( )
inline

Deprecated routine that returns torsionSigmaVector() as a human-readable string.

Deprecated:
This routine has been renamed to torsionSigmaVectorString(). See the torsionSigmaVectorString() documentation for further details.

§ h1CellAp()

const NHomMarkedAbelianGroup& regina::NHomologicalData::h1CellAp ( )

Returns the isomorphism from dualHomology(1) to homology(1) given by a cellular approximation to the identity map on the manifold.

Returns
The isomorphism from dualHomology(1) to homology(1) computed via a cellular approximation of the identity map from the first 1-skeleton to the second.

§ homology()

const NMarkedAbelianGroup& regina::NHomologicalData::homology ( unsigned  q)

This routine gives access to the manifold's homology computed with the regular CW-decomposition.

This routine is typically slower than dualHomology(), since dualHomology() uses the dual CW-decomposition which typically has an order of magnitude fewer cells.

Note that the groups returned by homology() and dualHomology() are isomorphic, though they are generally described by different presentations.

Parameters
qthe dimension of the homology group: can be 0, 1, 2 or 3.
Returns
the q-th homology group, computed in the standard CW-decomposition.

§ str()

std::string regina::Output< NHomologicalData , supportsUtf8 >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python:
In addition to str(), this is also used as the Python "stringification" function __str__().
Returns
a short text representation of this object.

§ torsionLegendreSymbolVector()

const std::vector< std::pair< NLargeInteger, std::vector< int > > > & regina::NHomologicalData::torsionLegendreSymbolVector ( )
inline

Returns the odd p-torsion Legendre symbol vector.

This is the last of the three Kawauchi-Kojima invariants.

For details, see "Algebraic classification of linking pairings on 3-manifolds", Akio Kawauchi and Sadayoshi Kojima, Math. Ann. 253 (1980), 29–42.

Precondition
The triangulation is of a connected orientable 3-manifold.
Python:
Not available, though the string routine torsionLegendreSymbolVectorString() can still be used.
Returns
the Legendre symbol vector associated to the torsion linking form.

§ torsionLegendreSymbolVectorString()

const std::string & regina::NHomologicalData::torsionLegendreSymbolVectorString ( )
inline

Same as torsionLegendreSymbolVector() but returns as a human-readable string.

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
the Legendre symbol vector in human-readable form.

§ torsionRankVector()

const std::vector< std::pair< NLargeInteger, std::vector< unsigned long > > > & regina::NHomologicalData::torsionRankVector ( )
inline

Returns the torsion form rank vector.

This is the first of the three Kawauchi-Kojima complete invariants of the torsion linking form.

This vector describes the rank of the torsion subgroup of H1, given in prime power form. It is a vector of pairs (p, x), where p is a prime and x is its exponent.

For details, see "Algebraic classification of linking pairings on 3-manifolds", Akio Kawauchi and Sadayoshi Kojima, Math. Ann. 253 (1980), 29–42.

Precondition
The triangulation is of a connected orientable 3-manifold.
Python:
Not available, though the string routine torsionRankVectorString() can still be used.
Returns
the torsion form rank vector.

§ torsionRankVectorString()

const std::string & regina::NHomologicalData::torsionRankVectorString ( )
inline

Same as torsionRankVector() but returns as a human-readable string.

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
human-readable prime power factorization of the order of the torsion subgroup of H1.

§ torsionSigmaVector()

const std::vector< NLargeInteger > & regina::NHomologicalData::torsionSigmaVector ( )
inline

Returns the 2-torsion sigma vector.

This is the second of the three Kawauchi-Kojima invariants. It is orientation-sensitive.

For details, see "Algebraic classification of linking pairings on 3-manifolds", Akio Kawauchi and Sadayoshi Kojima, Math. Ann. 253 (1980), 29–42.

Precondition
The triangulation is of a connected orientable 3-manifold.
Python:
Not available, though the string routine torsionSigmaVectorString() can still be used.
Returns
the Kawauchi-Kojima sigma-vector.

§ torsionSigmaVectorString()

const std::string & regina::NHomologicalData::torsionSigmaVectorString ( )
inline

Same as torsionSigmaVector() but returns as a human-readable string.

This is an orientation-sensitive invariant.

Precondition
The triangulation is of a connected orientable 3-manifold.
Returns
the Kawauchi-Kojima sigma-vector in human readable form.

§ toString()

REGINA_DEPRECATED std::string regina::Output< NHomologicalData , supportsUtf8 >::toString ( ) const
inherited

A deprecated alias for str().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.

§ toStringLong()

REGINA_DEPRECATED std::string regina::Output< NHomologicalData , supportsUtf8 >::toStringLong ( ) const
inherited

A deprecated alias for detail().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.

§ utf8()

std::string regina::Output< NHomologicalData , supportsUtf8 >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

§ writeTextLong()

void regina::ShortOutput< NHomologicalData , false >::writeTextLong ( std::ostream &  out) const
inlineinherited

A default implementation for detailed output.

This routine simply calls T::writeTextShort() and appends a final newline.

Python:
Not present.
Parameters
outthe output stream to which to write.

§ writeTextShort()

void regina::NHomologicalData::writeTextShort ( std::ostream &  out) const

Writes a short text representation of this object to the given output stream.

Note this only writes pre-computed data. Thus if you have not yet asked NHomologicalData to compute anything about this triangulation, writeTextShort may be empty.

Python:
Not present.
Parameters
outthe output stream to which to write.

The documentation for this class was generated from the following file:

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).