Transversal base class corresponding to a base element $\alpha$ . More...

#include <transversal.h>

Inheritance diagram for permlib::Transversal< PERM >:

Classes
struct	TrivialAction
	action of a PERM on unsigned long element More...

Public Member Functions
	Transversal (unsigned int n)
	constructor
virtual	~Transversal ()
	virtual destructor
virtual PERM *	at (unsigned long val) const =0
	returns a transversal element such that $\alpha^u$ equals val
virtual bool	trivialByDefinition (const PERM &x, unsigned long to) const =0
	true if Schreier generator constructed from x and the transversal element related to "to" is trivial by defintion
virtual bool	contains (const unsigned long &val) const
	true iff there exists a transversal element mapping $\alpha$ to val
std::list< unsignedlong >::const_iterator	begin () const
	begin iterator of basic orbit
std::list< unsignedlong >::const_iterator	end () const
	end iterator of basic orbit
std::pair< std::list< unsigned long >::const_iterator, std::list< unsigned long >::const_iterator >	pairIt () const
	pair of begin, end iterator
size_t	size () const
	size of basic orbit / transversal
unsigned int	n () const
	size of the set the group is working on
template<class InputIterator>
void	sort (InputIterator Bbegin, InputIterator Bend)
	sorts orbit according to order given by list of points
bool	sorted () const
	true iff orbit is sorted
virtual void	orbit (unsigned long alpha, const std::list< typename PERM::ptr > &generators)
	computes transversal based on orbit of $\alpha$ under generators
virtual void	orbitUpdate (unsigned long alpha, const std::list< typename PERM::ptr > &generators, const typename PERM::ptr &g)
	updates transversal based on orbit of $\alpha$ under generators where g is a new generator
virtual void	permute (const PERM &g, const PERM &gInv)
	updates transversal after group generators have been conjugated by g
virtual void	updateGenerators (const std::map< PERM *, typename PERM::ptr > &generatorChange)
	updates transversal after group generators have been exchanged
virtual const unsigned long &	element () const
	returns one element of the orbit

Protected Member Functions
virtual void	registerMove (unsigned long from, unsigned long to, const typename PERM::ptr &p)
	stores that 'p' maps 'from' onto 'to'
virtual bool	foundOrbitElement (const unsigned long &alpha, const unsigned long &alpha_p, const typename PERM::ptr &p)
	callback when the orbit algorithm constructs an element alpha_p from alpha and p
Protected Member Functions inherited from permlib::Orbit< PERM, unsigned long >
void	orbit (const unsigned long &beta, const std::list< typename PERM::ptr > &generators, Action a, std::list< unsigned long > &orbitList)
	computes orbit of beta under generators
void	orbitUpdate (const unsigned long &beta, const std::list< typename PERM::ptr > &generators, const typename PERM::ptr &g, Action a, std::list< unsigned long > &orbitList)
	updates an existing orbit of beta after one element has been added

Protected Attributes
unsigned int	m_n
	size of the set the group is working on
std::vector< boost::shared_ptr< PERM > >	m_transversal
	transversal elements
std::list< unsigned long >	m_orbit
	orbit elements
bool	m_sorted
	true if orbit is sorted (according to a previous sort(InputIterator, InputIterator) call

Friends
std::ostream &	operator<< (std::ostream &out, const Transversal< PERM > &p)
	to stream

Additional Inherited Members
Public Types inherited from permlib::Orbit< PERM, unsigned long >
typedef PERM	PERMtype
	type of permutation used for this orbit

Detailed Description

template<class PERM>
class permlib::Transversal< PERM >

Transversal base class corresponding to a base element $\alpha$ .

Constructor & Destructor Documentation

◆ Transversal()

template<class PERM>

permlib::Transversal< PERM >::Transversal ( unsigned int n )

constructor

Parameters

n	size of the set the group is working on

Member Function Documentation

◆ at()

template<class PERM>

virtual PERM * permlib::Transversal< PERM >::at ( unsigned long val ) const

pure virtual

returns a transversal element such that $\alpha^u$ equals val

Implemented in permlib::ExplicitTransversal< PERM >, permlib::SchreierTreeTransversal< PERM >, and permlib::SchreierTreeTransversal< PERMUTATION >.

◆ contains()

template<class PERM>

bool permlib::Transversal< PERM >::contains ( const unsigned long & val ) const

virtual

true iff there exists a transversal element mapping $\alpha$ to val

Implements permlib::Orbit< PERM, unsigned long >.

◆ element()

template<class PERM>

const unsigned long & permlib::Transversal< PERM >::element ( ) const

inlinevirtual

returns one element of the orbit

Implements permlib::Orbit< PERM, unsigned long >.

◆ foundOrbitElement()

template<class PERM>

bool permlib::Transversal< PERM >::foundOrbitElement	(	const unsigned long &	alpha,
		const unsigned long &	alpha_p,
		const typename PERM::ptr &	p )

protectedvirtual

callback when the orbit algorithm constructs an element alpha_p from alpha and p

Returns: true iff alpha_p is a new element that has not been seen before

Implements permlib::Orbit< PERM, unsigned long >.

◆ orbit()

template<class PERM>

void permlib::Transversal< PERM >::orbit	(	unsigned long	alpha,
		const std::list< typename PERM::ptr > &	generators )

virtual

computes transversal based on orbit of $\alpha$ under generators

Parameters

alpha	$\alpha$
generators	group generators for the orbit

Reimplemented in permlib::ShallowSchreierTreeTransversal< PERM >.

◆ orbitUpdate()

template<class PERM>

void permlib::Transversal< PERM >::orbitUpdate	(	unsigned long	alpha,
		const std::list< typename PERM::ptr > &	generators,
		const typename PERM::ptr &	g )

virtual

updates transversal based on orbit of $\alpha$ under generators where g is a new generator

Parameters

alpha	$\alpha$
generators	group generators for the orbit
g	new generator that the transversal is updated for

Reimplemented in permlib::ShallowSchreierTreeTransversal< PERM >.

◆ permute()

template<class PERM>

void permlib::Transversal< PERM >::permute	(	const PERM &	g,
		const PERM &	gInv )

virtual

updates transversal after group generators have been conjugated by g

Parameters

g	permutation to conjugate
gInv	inverse of g for performance reasons

Reimplemented in permlib::ExplicitTransversal< PERM >, and permlib::ShallowSchreierTreeTransversal< PERM >.

◆ registerMove()

template<class PERM>

void permlib::Transversal< PERM >::registerMove	(	unsigned long	from,
		unsigned long	to,
		const typename PERM::ptr &	p )

protectedvirtual

stores that 'p' maps 'from' onto 'to'

Reimplemented in permlib::ExplicitTransversal< PERM >, and permlib::SchreierTreeTransversal< PERM >.

◆ sort()

template<class PERM>

template<class InputIterator>

void permlib::Transversal< PERM >::sort	(	InputIterator	Bbegin,
		InputIterator	Bend )

sorts orbit according to order given by list of points

Parameters

Bbegin	begin iterator of point list (unsigned long) inducing an order
Bend	end iterator of point list (unsigned long) inducing an order

◆ trivialByDefinition()

template<class PERM>

virtual bool permlib::Transversal< PERM >::trivialByDefinition	(	const PERM &	x,
		unsigned long	to ) const

pure virtual

true if Schreier generator constructed from x and the transversal element related to "to" is trivial by defintion

Implemented in permlib::ExplicitTransversal< PERM >, and permlib::SchreierTreeTransversal< PERM >.

◆ updateGenerators()

template<class PERM>

virtual void permlib::Transversal< PERM >::updateGenerators ( const std::map< PERM *, typename PERM::ptr > & generatorChange )

inlinevirtual

updates transversal after group generators have been exchanged

Parameters

generatorChange map of old generators to new generators

Reimplemented in permlib::SchreierTreeTransversal< PERM >, and permlib::ShallowSchreierTreeTransversal< PERM >.

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

include/permlib/transversal/transversal.h

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Transversal()

Member Function Documentation

◆ at()

◆ contains()

◆ element()

◆ foundOrbitElement()

◆ orbit()

◆ orbitUpdate()

◆ permute()

◆ registerMove()

◆ sort()

◆ trivialByDefinition()

◆ updateGenerators()