Regina Calculation Engine
Public Member Functions | Static Public Member Functions | Protected Attributes | List of all members
regina::NGroupPresentation Class Reference

Represents a finite presentation of a group. More...

#include <algebra/ngrouppresentation.h>

Inheritance diagram for regina::NGroupPresentation:
regina::ShareableObject regina::boost::noncopyable

Public Member Functions

 NGroupPresentation ()
 Creates a new presentation with no generators and no relations. More...
 
 NGroupPresentation (const NGroupPresentation &cloneMe)
 Creates a clone of the given group presentation. More...
 
virtual ~NGroupPresentation ()
 Destroys the group presentation. More...
 
unsigned long addGenerator (unsigned long numToAdd=1)
 Adds one or more generators to the group presentation. More...
 
void addRelation (NGroupExpression *rel)
 Adds the given relation to the group presentation. More...
 
unsigned long getNumberOfGenerators () const
 Returns the number of generators in this group presentation. More...
 
unsigned long getNumberOfRelations () const
 Returns the number of relations in this group presentation. More...
 
const NGroupExpressiongetRelation (unsigned long index) const
 Returns the relation at the given index in this group presentation. More...
 
bool intelligentSimplify ()
 Attempts to simplify the group presentation as intelligently as possible without further input. More...
 
std::string recogniseGroup () const
 Attempts to recognise the group corresponding to this presentation. More...
 
void writeXMLData (std::ostream &out) const
 Writes a chunk of XML containing this group presentation. More...
 
void writeToFile (NFile &out) const
 Writes this group presentation to the given old-style binary file. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing. More...
 
virtual ~ShareableObject ()
 Default destructor that does nothing. More...
 
std::string toString () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toStringLong () const
 Returns the output from writeTextLong() as a string. More...
 

Static Public Member Functions

static NGroupPresentationreadFromFile (NFile &in)
 Reads a group presentation from the given old-style binary file. More...
 

Protected Attributes

unsigned long nGenerators
 The number of generators. More...
 
std::vector< NGroupExpression * > relations
 The relations between the generators. More...
 

Additional Inherited Members

- Protected Member Functions inherited from regina::boost::noncopyable
 noncopyable ()
 A constructor which does nothing. More...
 
 ~noncopyable ()
 A destructor which does nothing. More...
 

Detailed Description

Represents a finite presentation of a group.

A presentation consists of a number of generators and a set of relations between these generators that together define the group.

If there are g generators, they will be numbered 0, 1, ..., g-1.

Test:
Included in the test suite.
Todo:
Optimise (long-term): The simplification routines really need work!

Constructor & Destructor Documentation

regina::NGroupPresentation::NGroupPresentation ( )
inline

Creates a new presentation with no generators and no relations.

regina::NGroupPresentation::NGroupPresentation ( const NGroupPresentation cloneMe)

Creates a clone of the given group presentation.

Parameters
cloneMethe presentation to clone.
regina::NGroupPresentation::~NGroupPresentation ( )
inlinevirtual

Destroys the group presentation.

All relations that are stored will be deallocated.

Member Function Documentation

unsigned long regina::NGroupPresentation::addGenerator ( unsigned long  numToAdd = 1)
inline

Adds one or more generators to the group presentation.

If the new presentation has g generators, the new generators will be numbered g-1, g-2 and so on.

Parameters
numToAddthe number of generators to add.
Returns
the number of generators in the new presentation.
void regina::NGroupPresentation::addRelation ( NGroupExpression rel)
inline

Adds the given relation to the group presentation.

The relation must be of the form expression = 1.

This presentation will take ownership of the given expression, may change it and will be responsible for its deallocation.

Python:
Since this group presentation takes ownership of the given expression, the python object containing the given expression becomes a null object and should no longer be used.
Parameters
relthe expression that the relation sets to 1; for instance, if the relation is g1^2 g2 = 1 then this parameter should be the expression g1^2 g2.
unsigned long regina::NGroupPresentation::getNumberOfGenerators ( ) const
inline

Returns the number of generators in this group presentation.

Returns
the number of generators.
unsigned long regina::NGroupPresentation::getNumberOfRelations ( ) const
inline

Returns the number of relations in this group presentation.

Returns
the number of relations.
const NGroupExpression & regina::NGroupPresentation::getRelation ( unsigned long  index) const
inline

Returns the relation at the given index in this group presentation.

The relation will be of the form expresson = 1.

Parameters
indexthe index of the desired relation; this must be between 0 and getNumberOfRelations()-1 inclusive.
Returns
the expression that the requested relation sets to 1; for instance, if the relation is g1^2 g2 = 1 then this will be the expression g1^2 g2.
bool regina::NGroupPresentation::intelligentSimplify ( )

Attempts to simplify the group presentation as intelligently as possible without further input.

As with the NTriangulation routine of the same name, this routine is not as intelligent as it makes out to be. In fact, currently it does almost nothing.

Todo:
Feature (long-term): Make this simplification more effective.
Returns
true if and only if the group presentation was changed.
static NGroupPresentation* regina::NGroupPresentation::readFromFile ( NFile in)
static

Reads a group presentation from the given old-style binary file.

The presentation will be newly allocated, and responsibility for its destruction lies with the caller of this routine.

Deprecated:
For the preferred way of reading group presentations from file, see class NXMLGroupPresentationReader instead.
Precondition
The given file is currently opened for reading.
Python:
Not present.
Parameters
inthe file from which to read.
Returns
a newly allocated presentation read from the given file, or 0 if problems arose.
std::string regina::NGroupPresentation::recogniseGroup ( ) const

Attempts to recognise the group corresponding to this presentation.

This routine is much more likely to be successful if you have already called intelligentSimplify().

Note that the presentation might be simplified a little during the execution of this routine, although not nearly as much as would be done by intelligentSimplify().

Todo:
Feature (long-term): Make this recognition more effective.
Returns
a simple string representation of the group if it is recognised, or an empty string if the group is not recognised.
virtual void regina::NGroupPresentation::writeTextLong ( std::ostream &  out) const
virtual

Writes this object in long text format to the given output stream.

The output should provided the user with all the information they could want. The output should end with a newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Reimplemented from regina::ShareableObject.

void regina::NGroupPresentation::writeTextShort ( std::ostream &  out) const
inlinevirtual

Writes this object in short text format to the given output stream.

The output should fit on a single line and no newline should be written.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Implements regina::ShareableObject.

void regina::NGroupPresentation::writeToFile ( NFile out) const

Writes this group presentation to the given old-style binary file.

Deprecated:
For the preferred way to write data to file, see writeXMLData() instead.
Precondition
The given file is currently opened for writing.
Python:
Not present.
Parameters
outthe file to which to write.
void regina::NGroupPresentation::writeXMLData ( std::ostream &  out) const

Writes a chunk of XML containing this group presentation.

Python:
Not present.
Parameters
outthe output stream to which the XML should be written.

Member Data Documentation

unsigned long regina::NGroupPresentation::nGenerators
protected

The number of generators.

std::vector<NGroupExpression*> regina::NGroupPresentation::relations
protected

The relations between the generators.


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

Copyright © 1999-2012, The Regina development team
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).