permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer > Class Template Reference

BSGS construction with Random Schreier-Sims algorithm. More...

#include <random_schreier_sims_construction.h>

Inheritance diagram for permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer >:

Public Member Functions
	RandomSchreierSimsConstruction (unsigned int n, RandomGenerator< PERM > *rng, Integer knownOrder=0, unsigned int minimalConsecutiveSiftingElementCount=20, unsigned int maxIterationFactor=10000)
	constructor More...
template<class ForwardIterator >
BSGS< PERM, TRANS >	construct (ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, bool &guaranteedBSGS) const
	constructs a probable BSGS for group given by generators with no base prescribed More...
template<class ForwardIterator , class InputIterator >
BSGS< PERM, TRANS >	construct (ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd, bool &guaranteedBSGS) const
	constructs a probable BSGS for group given by generators respecting prescribed base elements More...
Public Member Functions inherited from permlib::BaseConstruction< PERM, TRANS >
	BaseConstruction (dom_int n)
	constructor More...

Public Attributes
unsigned int	m_statRandomElementsConsidered
	number of Schreier generators examined during the last construct call
const unsigned int	m_minimalConsecutiveSiftingElementCount
	number of elements that have to sift through constructed BSGS consecutively that it is returned as a probable BSGS
const unsigned int	m_maxIterationFactor
	factor limiting the number of maximal iterations depeding on the initial base size

Additional Inherited Members
Protected Member Functions inherited from permlib::BaseConstruction< PERM, TRANS >
template<class ForwardIterator , class InputIterator >
void	setup (ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd, BSGS< PERM, TRANS > &bsgs, std::vector< std::list< typename PERM::ptr > > &S) const
	initializes BSGS object More...
void	mergeGenerators (std::vector< std::list< typename PERM::ptr > > &S, BSGS< PERM, TRANS > &ret) const
	merges all strong generators in S into a single strong generating set ret.S
Protected Attributes inherited from permlib::BaseConstruction< PERM, TRANS >
dom_int	m_n
	cardinality of the set the group is acting on
Static Protected Attributes inherited from permlib::BaseConstruction< PERM, TRANS >
static const unsigned long *	empty = static_cast<unsigned long*>(0)
	auxilliary element marking an empty iterator

Detailed Description

template<class PERM, class TRANS, typename Integer = boost::uint64_t>
class permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer >

BSGS construction with Random Schreier-Sims algorithm.

Randomized algorithm for BSGS construction. If order is known it is Las Vegas type, otherwise Monte Carlo (it may return an incomplete BSGS).

Constructor & Destructor Documentation

RandomSchreierSimsConstruction()

template<class PERM , class TRANS , typename Integer >

permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer >::RandomSchreierSimsConstruction	(	unsigned int	n,
		RandomGenerator< PERM > *	rng,
		Integer	knownOrder = 0,
		unsigned int	minimalConsecutiveSiftingElementCount = 20,
		unsigned int	maxIterationFactor = 10000
	)

constructor

Parameters

n	cardinality of the set the group is acting on
rng	a RandomGenerator generating uniformly distributed random group elements of the group that the BSGS is constructed of
knownOrder	order of the group that the BSGS is constructed of. If non-zero upgrades algorithm to Las Vegas type and the output is guaranteed to be a BSGS.
minimalConsecutiveSiftingElementCount	number of elements that have to sift through constructed BSGS consecutively that it is returned as a probable BSGS
maxIterationFactor	factor limiting the number of maximal iterations depeding on the initial base size

Member Function Documentation

construct() [1/2]

template<class PERM , class TRANS , typename Integer >

template<class ForwardIterator >

BSGS< PERM, TRANS > permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer >::construct ( ForwardIterator  generatorsBegin, ForwardIterator  generatorsEnd, bool &  guaranteedBSGS  ) const

inline

constructs a probable BSGS for group given by generators with no base prescribed

See also

construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd, bool& guaranteedBSGS)

construct() [2/2]

template<class PERM , class TRANS , typename Integer >

template<class ForwardIterator , class InputIterator >

BSGS< PERM, TRANS > permlib::RandomSchreierSimsConstruction< PERM, TRANS, Integer >::construct	(	ForwardIterator	generatorsBegin,
		ForwardIterator	generatorsEnd,
		InputIterator	prescribedBaseBegin,
		InputIterator	prescribedBaseEnd,
		bool &	guaranteedBSGS
	)		const

constructs a probable BSGS for group given by generators respecting prescribed base elements

runs (#{size of initial base} * maxIterationFactor) iterations or until constructed BSGS has knownOrder or #minimalConsecutiveSiftingElementCount sift through the constructed BSGS consecutively

Parameters

generatorsBegin	begin iterator of group generators of type PERM
generatorsEnd	end iterator of group generators of type PERM
prescribedBaseBegin	begin iterator of prescribed base of type unsigned long
prescribedBaseEnd	end iterator of prescribed base of type unsigned long
guaranteedBSGS	iff true, return object is guaranteed to be a BSGS

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

• include/permlib/construct/random_schreier_sims_construction.h