LatBuilder::GenSeq::CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER > Class Template Reference

Inherits LatBuilder::Traversal::Policy< CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER >, TRAV >.

Classes
struct	RebindTraversal
	Rebinds the traversal type. More...

Public Types
typedef CyclicGroupTraits< self_type >::size_type	size_type
typedef CyclicGroupTraits< self_type >::value_type	value_type
typedef CyclicGroupTraits< self_type >::Modulus	Modulus
typedef TRAV	Traversal
	Traversal type.

Public Member Functions
	CyclicGroup (Traversal trav=Traversal())
	Constructor for an empty group.
	CyclicGroup (Modulus base, Level power, Traversal trav=Traversal())
	Constructor for the cyclic group of integers modulo \(b^m\), where \(b\) is a prime base. More...
template<class TRAV2 >
	CyclicGroup (const CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV2, ORDER > &other, Traversal trav=Traversal())
	Cross-traversal copy-constructor.
template<class TRAV2 >
RebindTraversal< TRAV2 >::Type	rebind (TRAV2 trav) const
	Returns a copy of this object, but using a different traversal policy.
Modulus	base () const
	Returns the base of the group modulus.
Level	power () const
	Returns the power of the base of the group modulus.
size_type	fullSize () const
	Returns the cardinality of the full group. More...
size_type	size () const
	Returns the cardinality of the group part specified by COMPRESS.
Modulus	modulus () const
	Returns the modulus \(b^m\) of the cyclic group.
value_type	generator () const
	Returns the generator \(g\) for the group.
value_type	operator[] (size_type i) const
	Returns the element at index i.
CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, !ORDER >	inverse () const
	Returns the group generated by the inverse generator.
CyclicGroup	subgroup (Level level) const
	Returns the subgroup at level level.
template<Compress COMPRESS, class TRAV , GroupOrder ORDER>
	CyclicGroup (const CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER > &other, Level level)

Static Public Member Functions
static constexpr LatBuilder::Compress	compress ()
static std::string	name ()
static value_type	smallestGenerator (Modulus base, Level power, bool checkPrime=true)
	Returns the smallest generator for the group of cyclic integers modulo \(b^m\). More...

Friends
template<LatticeType , LatBuilder::Compress , class , GroupOrder >
class	CyclicGroup
class	CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, !ORDER >

Constructor & Destructor Documentation

CyclicGroup()

template<Compress COMPRESS, class TRAV , GroupOrder ORDER>

LatBuilder::GenSeq::CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER >::CyclicGroup	(	Modulus	base,
		Level	power,
		Traversal	trav = Traversal()
	)

Constructor for the cyclic group of integers modulo \(b^m\), where \(b\) is a prime base.

Parameters

base	Prime base \(b\).
power	Power \(m\) of the base.
trav	Traversal instance.

References LatBuilder::intPow().

Member Function Documentation

fullSize()

template<Compress COMPRESS, class TRAV , GroupOrder ORDER>

size_type LatBuilder::GenSeq::CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER >::fullSize ( ) const

inline

Returns the cardinality of the full group.

Remarks

If COMPRESS is Compress::NONE, this is the same as size().

smallestGenerator()

template<Compress COMPRESS, class TRAV , GroupOrder ORDER>

CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER >::value_type LatBuilder::GenSeq::CyclicGroup< LatticeType::ORDINARY, COMPRESS, TRAV, ORDER >::smallestGenerator ( Modulus  base, Level  power, bool  checkPrime = true  )

static

Returns the smallest generator for the group of cyclic integers modulo \(b^m\).

Parameters

base	\(b\)
power	\(m\)
checkPrime	If true, checks if the base is actually prime.

The algorithm is described in [2] .

References LatBuilder::modularPow(), LatticeTester::power(), and LatBuilder::primeFactors().

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

• include/latbuilder/GenSeq/CyclicGroup-OLR.h