regina Namespace Reference

Contains the entire Regina calculation engine. More...

Namespaces
namespace	alias
	Contains helper classes that provide dimension-specific aliases for generic functions.
namespace	detail
	Contains implementation details and common functionality for Regina's dimension-agnostic classes.
namespace	i18n
	Various classes and routines for working with internationalisation and character encodings.
namespace	xml
	Various classes and routines for XML manipulation, some taken or modified from the libxml++ library.

Classes
class	AbelianGroup
	Represents a finitely generated abelian group. More...
class	AngleStructure
	Represents an angle structure on a triangulation. More...
class	AngleStructures
	A collection of angle structures on a 3-manifold triangulation. More...
class	Attachment
	A packet that can hold an arbitrary file attachment. More...
class	AugTriSolidTorus
	Represents an augmented triangular solid torus component of a triangulation. More...
class	BanBoundary
	A class that bans normal disc types that meet the boundary of the underlying triangulation. More...
class	BanConstraintBase
	A base class for additional banning and marking constraints that we can place on tree traversal algorithms. More...
class	BanEdge
	A class that bans normal disc types that meet a particular edge of the underlying triangulation. More...
class	BanNone
	A do-nothing class that bans no coordinates and marks no coordinates. More...
class	BanTorusBoundary
	A class that bans and marks disc types associated with torus boundary components. More...
struct	Base64SigEncoding
	General helper tools for signatures that use base64 encodings. More...
class	BitManipulator
	An optimised class for bitwise analysis and manipulation of native data types. More...
class	BitManipulatorBySize
	Contains implementation details for BitManipulator where we optimise according to the size of the underlying data type. More...
class	BitManipulatorByType
	Contains implementation details for BitManipulator where we optimise according to the underlying data type. More...
class	Bitmask
	A bitmask that can store arbitrarily many true-or-false bits. More...
class	Bitmask1
	A small but extremely fast bitmask class that can store up to 8 * sizeof(T) true-or-false bits. More...
class	Bitmask2
	A small but extremely fast bitmask class that can store up to 8 * sizeof(T) + 8 * sizeof(U) true-or-false bits. More...
class	BlockedSFS
	Represents a blocked Seifert fibred space (possibly with boundary). More...
class	BlockedSFSLoop
	Represents a blocked Seifert fibred space with two boundary tori that are joined together. More...
class	BlockedSFSPair
	Represents a blocked pair of Seifert fibred spaces joined along a single connecting torus. More...
class	BlockedSFSTriple
	Represents a blocked sequence of three Seifert fibred spaces joined along connecting tori. More...
class	BoolSet
	A set of booleans. More...
class	BoundaryComponent
	A component of the boundary of a dim-manifold triangulation. More...
struct	CallableArg
	A traits class that deduces the type of the argument in a given position for a callable object. More...
class	Census
	A utility class used to search for triangulations across one or more 3-manifold census databases. More...
class	CensusDB
	Stores the location and description of one of Regina's in-built census databases. More...
class	CensusHit
	Stores a single "hit" indicating that some given triangulation has been located in one of Regina's in-built census databases. More...
class	ChildIterator
	A forward iterator for iterating through all immediate children of a given packet. More...
class	ClosedPrimeMinSearcher
	A gluing permutation search class that offers a specialised search algorithm for when (i) only closed prime minimal P2-irreducible triangulations are required, and (ii) the given face pairing has order at least three. More...
class	CompactSearcher
	A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3-manifold triangulations are required. More...
class	Component
	A connected component of a dim-manifold triangulation. More...
class	Component< 2 >
	Represents a connected component of a 2-manifold triangulation. More...
class	Component< 3 >
	Represents a connected component of a 3-manifold triangulation. More...
class	Component< 4 >
	Represents a connected component of a 4-manifold triangulation. More...
class	Container
	A packet that simply contains other packets. More...
class	Crossing
	Represents a single crossing in a link diagram. More...
class	Cusp
	Used to return information about a single cusp of a SnapPea triangulation. More...
class	Cut
	A cut that separates a triangulation or facet pairing into two pieces. More...
class	Cyclotomic
	Represents an element of a cyclotomic field. More...
class	DegreeGreaterThan
	Deprecated function object used for sorting faces of triangulations by decreasing degree. More...
class	DegreeLessThan
	Deprecated function object used for sorting faces of triangulations by increasing degree. More...
class	DiscSetSurfaceDataImpl
	Stores a piece of data alongside every normal disc within a particular normal surface. More...
class	DiscSetTet
	Represents a set of normal discs inside a single tetrahedron. More...
class	DiscSetTetData
	Stores data of type T for every normal disc inside a single tetrahedron. More...
struct	DiscSpec
	Specifies a single normal disc in a normal surface. More...
class	DiscSpecIterator
	A forward iterator used for running through all normal discs in a normal surface. More...
struct	DiscType
	Identifies a single normal or almost normal disc type within a triangulation. More...
class	DoubleDescription
	Implements a modified double description method for polytope vertex enumeration. More...
struct	EnableIf
	A struct that holds either a single value of type T or nothing at all, depending on whether the given compile-time condition holds. More...
class	EulerSearcher
	A gluing permutation search class that offers a specialised search algorithm for when all vertex links must all have a given fixed Euler characteristic. More...
class	Example
	This class offers static routines for constructing a variety of sample dim-dimensional triangulations. More...
class	Example< 2 >
	Offers routines for constructing a variety of sample 2-dimensional triangulations. More...
class	Example< 3 >
	Offers routines for constructing a variety of sample 3-dimensional triangulations. More...
class	Example< 4 >
	Offers routines for constructing a variety of sample 4-dimensional triangulations. More...
class	ExampleLink
	This class offers routines for constructing ready-made examples of knots and links. More...
class	ExampleSnapPea
	This class offers routines for constructing various example SnapPea triangulations. More...
class	Face
	Represents a subdim-face in the skeleton of a dim-dimensional triangulation. More...
class	Face< 2, 2 >
	Represents a triangle within a 2-manifold triangulation. More...
class	Face< 3, 0 >
	Represents a vertex in the skeleton of a 3-manifold triangulation. More...
class	Face< 3, 1 >
	Represents an edge in the skeleton of a 3-manifold triangulation. More...
class	Face< 3, 2 >
	Represents a triangle in the skeleton of a 3-manifold triangulation. More...
class	Face< 3, 3 >
	Represents a tetrahedron within a 3-manifold triangulation. More...
class	Face< 4, 0 >
	Represents a vertex in the skeleton of a 4-manifold triangulation. More...
class	Face< 4, 1 >
	Represents an edge in the skeleton of a 4-manifold triangulation. More...
class	Face< 4, 2 >
	Represents a triangle in the skeleton of a 4-manifold triangulation. More...
class	Face< 4, 3 >
	Represents a tetrahedron in the skeleton of a 4-manifold triangulation. More...
class	Face< 4, 4 >
	Represents a pentachoron (a 4-dimensional simplex) within a 4-manifold triangulation. More...
class	Face< dim, dim >
	Represents a top-dimensional simplex in a dim-manifold triangulation. More...
class	FaceEmbedding
	Details how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
class	FaceNumbering
	Specifies how subdim-faces are numbered within a dim-dimensional simplex. More...
class	FacePair
	Represents a pair of tetrahedron face numbers. More...
class	FacetPairing
	Represents the dual graph of a dim-manifold triangulation; that is, the pairwise matching of facets of dim-dimensional simplices. More...
class	FacetPairing< 3 >
	Represents the dual graph of a 3-manifold triangulation. More...
struct	FacetSpec
	A lightweight class used to refer to a particular facet of a particular top-dimensional simplex in a dim-dimensional triangulation. More...
class	FailedPrecondition
	An exception thrown when a function detects that its preconditions have been violated. More...
struct	FaithfulAssignment
	Determines if an integer of type From can always be assigned to an integer of type To with no loss of information. More...
class	FileError
	An exception thrown when trying to access data from the filesystem. More...
class	FileInfo
	Stores information about a Regina data file, including file format and version. More...
class	Flags
	A class representing a bitwise combination of flags defined by an enumeration type. More...
class	GlobalDirs
	Provides global routines that return directories in which various components of Regina are installed on the system. More...
class	GluingPerms
	Represents a specific set of gluing permutations to complement a particular pairwise matching of simplex facets. More...
class	GluingPermSearcher
	A utility class used to build a census of triangulations, by searching through all possible sets of gluing permutations to match a given facet pairing. More...
class	GluingPermSearcher< 2 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given triangle edge pairing. More...
class	GluingPermSearcher< 3 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given tetrahedron face pairing. More...
class	GluingPermSearcher< 4 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given pentachoron facet pairing. More...
class	GraphLoop
	Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus. More...
class	GraphPair
	Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More...
class	GraphTriple
	Represents a closed graph manifold formed by joining three bounded Seifert fibred spaces along their torus boundaries. More...
class	GroupExpression
	Represents an expression involving generators from a group presentation or a free group. More...
struct	GroupExpressionTerm
	Represents a power of a generator in a group presentation. More...
class	GroupPresentation
	Represents a finite presentation of a group. More...
class	Handlebody
	Represents an orientable handlebody. More...
class	HilbertCD
	Implements a modified Contejean-Devie algorithm for enumerating Hilbert bases. More...
class	HilbertDual
	Implements a modified dual algorithm for enumerating Hilbert bases. More...
class	HilbertPrimal
	Implements a modified primal algorithm for enumerating Hilbert bases. More...
class	HomGroupPresentation
	Represents a homomorphism between groups which are described via finite presentations. More...
class	HomMarkedAbelianGroup
	Represents a homomorphism of finitely generated abelian groups. More...
class	HomologicalData
	A specialised class that computes a large amount of detailed homological information for a 3-manifold triangulation. More...
class	HyperbolicMinSearcher
	A gluing permutation search class that offers a specialised search algorithm for when only minimal ideal triangulations of cusped finite-volume hyperbolic 3-manifolds are required. More...
class	HyperEncoding
	Indicates precisely how a normal hypersurface within a 4-manifold triangulation is encoded by an integer vector. More...
class	HyperInfo
	A class used to query general information about different normal hypersurface coordinate systems. More...
struct	InfinityBase
	Internal base classes for use with IntegerBase, templated on whether we should support infinity as an allowed value. More...
class	IntegerBase
	Represents an arbitrary precision integer. More...
class	IntersectionForm
	Represents a symmetric bilinear integral form, which for Regina is typically the intersection form of a 4-manifold. More...
struct	IntOfMinSize
	Gives access to native integer types that hold at least k bytes, where k may be any compile-time constant. More...
struct	IntOfSize
	Gives access to native integer types that hold exactly k bytes, where k may be any compile-time constant. More...
class	InvalidArgument
	An exception thrown when invalid or unsupported arguments are passed into a function. More...
class	InvalidInput
	An exception thrown when a function reads unexpected or incomplete data from an input stream. More...
class	Isomorphism
	Represents a combinatorial isomorphism from one dim-manifold triangulation into another. More...
class	IsoSigClassic
	The default signature type to use for isomorphism signatures. More...
class	IsoSigDegrees
	Defines an alternate type of isomorphism signature based on degree sequences of subdim-faces. More...
class	IsoSigPrintable
	The default encoding to use for isomorphism signatures. More...
struct	IsReginaArbitraryPrecisionInteger
	Determines if the type T is one of Regina's arbitrary precision integer types. More...
struct	IsReginaInteger
	Determines if the type T is one of Regina's own integer types (either arbitrary precision or fixed size). More...
class	Laurent
	Represents a single-variable Laurent polynomial with coefficients of type T. More...
class	Laurent2
	Represents a Laurent polynomial in the two variables x, y with coefficients of type T. More...
class	LayeredChain
	Represents a layered chain in a triangulation. More...
class	LayeredChainPair
	Represents a layered chain pair component of a triangulation. More...
class	LayeredLensSpace
	Represents a layered lens space component of a triangulation. More...
class	LayeredLoop
	Represents a layered loop component of a triangulation. More...
class	LayeredSolidTorus
	Represents a layered solid torus in a triangulation. More...
class	LayeredTorusBundle
	Describes a layered torus bundle. More...
class	Layering
	Represents a layering of zero or more tetrahedra upon a torus boundary. More...
class	LensSpace
	Represents a general lens space. More...
class	LightweightSequence
	A lightweight class for storing a random-access sequence of objects. More...
class	Link
	Represents a directed knot or link in the 3-sphere. More...
class	ListView
	A lightweight object that can be used for iteration and random access to all elements of a given list. More...
class	ListView< Element * >
	A specialisation of ListView for working with lists stored in a C-style array whose size is not known at compile-time. More...
class	ListView< Element[n]>
	A specialisation of ListView for working with lists stored in a C-style array whose size is fixed at compile-time. More...
struct	LPCol
	Used by LPInitialTableaux<LPConstraint> to store a single column of the adjusted matching equation matrix in sparse form. More...
class	LPConstraintBase
	A base class for additional linear constraints that we can add to the tableaux of normal surface or angle structure matching equations. More...
class	LPConstraintEulerPositive
	A class that constraints the tableaux of normal surface matching equations to ensure that Euler characteristic is strictly positive. More...
class	LPConstraintEulerZero
	A class that constraints the tableaux of normal surface matching equations to ensure that Euler characteristic is zero. More...
class	LPConstraintNone
	A do-nothing class that imposes no additional linear constraints on the tableaux of normal surface or angle structure matching equations. More...
class	LPConstraintNonSpun
	A class that constraints the tableaux of normal surface matching equations to ensure that normal surfaces in an ideal triangulation are compact (thereby avoiding spun normal surfaces with infinitely many triangles). More...
class	LPConstraintSubspace
	A subclass of LPConstraintBase used for constraints defined entirely by homogeneous linear equations. More...
class	LPData
	Stores an intermediate tableaux for the dual simplex method, and contains all of the core machinery for using the dual simplex method. More...
class	LPInitialTableaux
	Stores an adjusted matrix of homogeneous linear matching equations based on a given triangulation, in sparse form. More...
class	LPMatrix
	A matrix class for use with linear programming. More...
class	LPSystem
	Indicates which broad class of vector encodings a particular tableaux is designed to work with. More...
class	Manifold
	Represents a particular 3-manifold, independent of how it might be triangulated. More...
class	MarkedAbelianGroup
	Represents a finitely generated abelian group given by a chain complex. More...
class	MarkedElement
	A base class for elements of MarkedVector. More...
class	MarkedVector
	A vector of objects with fast, space-efficient reverse lookup of array indices. More...
class	Matrix
	Represents a matrix of elements of the given type T. More...
class	Matrix2
	Represents a 2-by-2 integer matrix. More...
class	MaxAdmissible
	Used to enumerate all maximal admissible faces of a polyhedral cone under a given set of admissibility constraints. More...
class	mem_istream
	An input stream that reads an array of characters in memory. More...
class	mem_streambuf
	A stream buffer that provides the implementation details for mem_istream. More...
class	ModelLinkGraph
	Represents an undirected 4-valent planar graph with a specific planar embedding. More...
class	ModelLinkGraphArc
	A reference to an outgoing edge from a node of a model graph for a knot or link. More...
class	ModelLinkGraphCells
	Describes the cellular decomposition of the sphere that is induced by a given planar 4-valent graph. More...
class	ModelLinkGraphNode
	Represents a single node in a model graph for a knot or link. More...
class	NativeInteger
	A wrapper class for a native, fixed-precision integer type of the given size. More...
class	NormalEncoding
	Indicates precisely how a normal surface is encoded by an integer vector. More...
class	NormalHypersurface
	Represents a single normal hypersurface in a 4-manifold triangulation. More...
class	NormalHypersurfaces
	A collection of normal hypersurfaces in a 4-manifold triangulation. More...
class	NormalInfo
	A class used to query general information about different normal coordinate systems. More...
class	NormalSurface
	Represents a single normal surface in a 3-manifold triangulation. More...
class	NormalSurfaces
	A collection of normal surfaces in a 3-manifold triangulation. More...
class	NoSolution
	An exception thrown when Regina has certified that a mathematical problem has no solution. More...
class	NotImplemented
	An exception thrown when some functionality is not yet implemented. More...
struct	Output
	A common base class for objects that write human-readable text output. More...
struct	OutputBase
	Provides a type alias to help identify where in the class hierarchy the output functions T::str() and T::detail() are implemented. More...
class	Packet
	Represents a packet of information that may be individually edited or operated upon. More...
class	PacketChildren
	A lightweight object that gives access to all immediate children of a given packet. More...
class	PacketData
	A lightweight helper class that allows an object of type Held to connect with the wrapped packet class that contains it. More...
class	PacketDescendants
	A lightweight object that gives access to all strict descendants of a given packet. More...
class	PacketInfo
	A class used to query general information about different packet types. More...
class	PacketListener
	An object that can be registered to listen for packet events. More...
class	PacketOf
	A packet that stores a mathematical object of type Held. More...
class	PacketShell
	Gives access to the final remains of a packet that is in the process of being destroyed. More...
class	Perm
	Represents a permutation of {0,1,...,n-1}. More...
class	Perm< 2 >
	Represents a permutation of {0,1}. More...
class	Perm< 3 >
	Represents a permutation of {0,1,2}. More...
class	Perm< 4 >
	Represents a permutation of {0,1,2,3}. More...
class	Perm< 5 >
	Represents a permutation of {0,1,2,3,4}. More...
class	Perm< 6 >
	Represents a permutation of {0,1,2,3,4,5}. More...
class	Perm< 7 >
	Represents a permutation of {0,1,2,3,4,5,6}. More...
class	PermClass
	Represents a conjugacy class of permutations on n elements. More...
class	PermGroup
	Represents a group of permutations on n elements. More...
class	PillowTwoSphere
	Represents a 2-sphere made from two triangles glued together along their three edges. More...
class	PluggedTorusBundle
	Describes a triangulation of a graph manifold formed by joining a bounded saturated region with a thin I-bundle over the torus, possibly with layerings in between. More...
class	PlugTriSolidTorus
	Represents a plugged triangular solid torus component of a triangulation. More...
class	Polynomial
	Represents a single-variable polynomial with coefficients of type T. More...
class	PosOrder
	A comparison object that sorts hyperplanes by position vectors. More...
class	Primes
	A helper class for finding primes and factorising integers. More...
struct	PrismSpec
	Specifies a single triangular prism in a tetrahedron. More...
class	ProgressTracker
	Manages percentage-based progress tracking and cancellation polling for long operations. More...
class	ProgressTrackerBase
	The base class for Regina's progress tracking classes. More...
class	ProgressTrackerOpen
	Manages percentage-based progress tracking and cancellation polling for open-ended operations. More...
class	Qitmask1
	A small but extremely fast "base 4 bitmask" class that can store up to 8 * sizeof(T) "qits", each equal to 0, 1, 2 or 3. More...
class	Qitmask2
	A small but extremely fast "base 4 bitmask" class that can store up to 8 * sizeof(T) + 8 * sizeof(U) "qits", each equal to 0, 1, 2 or 3. More...
class	RandomEngine
	Offers threadsafe access to Regina's global uniform random bit generator. More...
class	Rational
	Represents an arbitrary precision rational number. More...
class	ReginaException
	A base class for all of the exceptions that are thrown by Regina's native mathematical code. More...
struct	SatAnnulus
	Represents an annulus formed from a pair of triangles in a Seifert fibred space. More...
class	SatBlock
	Represents a saturated block in a Seifert fibred space. More...
class	SatBlockModel
	Contains an explicit triangulation of a saturated block along with the accompanying saturated block description. More...
class	SatBlockSpec
	Describes how a single saturated block forms a part of a larger saturated region. More...
class	SatCube
	A saturated block that is a six-tetrahedron cube. More...
class	SatLayering
	A degenerate saturated block that is a single tetrahedron wrapped around so that two opposite edges touch. More...
class	SatLST
	A saturated block that is a layered solid torus. More...
class	SatMobius
	A degenerate zero-tetrahedron saturated block that corresponds to attaching a Mobius band to a single annulus boundary. More...
class	SatReflectorStrip
	A saturated block that is a reflector strip. More...
class	SatRegion
	A large saturated region in a Seifert fibred space formed by joining together saturated blocks. More...
class	SatTriPrism
	A saturated block that is a three-tetrahedron triangular prism. More...
class	Script
	A packet representing a Python script that can be run. More...
class	SFSAlt
	Provides an alternative representation of a single bounded Seifert fibred space. More...
struct	SFSFibre
	Represents an exceptional (alpha, beta) fibre in a Seifert fibred space. More...
class	SFSpace
	Represents a general Seifert fibred space, which may be orientable or non-orientable. More...
class	ShortArray
	A short stack-based array of bounded size. More...
struct	ShortOutput
	A common base class for objects that provide short text output only. More...
class	SigCensus
	A class responsible for building censuses of splitting surface signatures. More...
class	Signature
	Represents a signature of a splitting surface in a closed 3-manifold triangulation. More...
class	SigPartialIsomorphism
	Represents a partial isomorphism between two splitting surface signatures. More...
class	SimpleSurfaceBundle
	Represents a particularly simple closed surface bundle over the circle. More...
class	SnapPeaCensusManifold
	Represents a 3-manifold from the SnapPea cusped census. More...
class	SnapPeaCensusTri
	Represents a 3-manifold triangulation from the SnapPea cusped census. More...
class	SnapPeaFatalError
	An exception that is thrown when the SnapPea kernel encounters a fatal error. More...
class	SnapPeaIsNull
	An exception thrown when the SnapPea kernel is asked to work with a null SnapPea triangulation. More...
class	SnapPeaMemoryFull
	An exception that is thrown when the SnapPea kernel finds that all available memory has been exhausted. More...
class	SnapPeaTriangulation
	Offers direct access to the SnapPea kernel from within Regina. More...
class	SnapPeaUnsolvedCase
	An exception thrown when the SnapPea kernel is not able to perform some computation. More...
class	SnappedBall
	Represents a snapped 3-ball in a triangulation. More...
class	SnappedTwoSphere
	Represents a 2-sphere made from two snapped 3-balls in a triangulation. More...
class	Snapshot
	Keeps a snapshot of an object of type T as it was at a particular moment in time. More...
class	SnapshotRef
	A reference to an image of type T that has been snapshotted at a particular moment in time. More...
class	Snapshottable
	A base class for images of type T that can be snapshotted at a particular moment in time. More...
class	SnapshotWriteError
	An exception thrown when someone tries to modify the read-only deep copy taken by a snapshot. More...
class	SpiralSolidTorus
	Represents a spiralled solid torus in a triangulation. More...
class	StandardTriangulation
	Describes a triangulation or subcomplex of a triangulation whose structure is well-understood. More...
class	StrandRef
	A reference to one of the two strands of a link that pass each other at a crossing. More...
class	SubtreeIterator
	A forward iterator for iterating through the entire packet subtree rooted at a given packet. More...
class	SurfaceFilter
	A packet that accepts or rejects normal surfaces. More...
class	SurfaceFilterCombination
	A normal surface filter that simply combines other filters. More...
class	SurfaceFilterProperties
	A normal surface filter that filters by basic properties of the normal surface. More...
class	TableView
	A lightweight object that can be used for random access to all elements of a given multi-dimensional table. More...
class	Tangle
	Represents a 2-tangle in the 3-ball. More...
class	TautEnumeration
	The main entry point for the tree traversal algorithm to enumerate all taut angle structures in a 3-manifold triangulation. More...
class	Text
	A packet representing a text string. More...
struct	TightEncodable
	A base class that assists with support for tight encodings and corresponding decodings. More...
class	TorusBundle
	Represents a torus bundle over the circle. More...
class	TreeBag
	Represents a single bag in a tree decomposition. More...
class	TreeDecomposition
	Represents a tree decomposition of a graph. More...
class	TreeEnumeration
	The main entry point for the tree traversal algorithm to enumerate all vertex normal or almost normal surfaces in a 3-manifold triangulation. More...
class	TreeSingleSoln
	The main entry point for the tree traversal / branching algorithm to locate a single non-trivial normal surface satisfying given constraints within a 3-manifold triangulation. More...
class	TreeTraversal
	A base class for searches that employ the tree traversal algorithm for enumerating and locating vertex normal surfaces and taut angle structures. More...
class	Triangulation
	A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets. More...
class	Triangulation< 2 >
	Represents a 2-manifold triangulation. More...
class	Triangulation< 3 >
	Represents a 3-dimensional triangulation, typically of a 3-manifold. More...
class	Triangulation< 4 >
	Represents a 4-dimensional triangulation, typically of a 4-manifold. More...
class	TrieSet
	A trie-like data structure for storing and retriving sets. More...
class	TriSolidTorus
	Represents a three-tetrahedron triangular solid torus in a triangulation. More...
class	TrivialTri
	Represents one of a few particular hard-coded trivial triangulations that do not belong to any of the other larger families. More...
class	TxICore
	Provides a triangulation of the product T x I (the product of the torus and the interval). More...
class	TxIDiagonalCore
	One of a family of thin T x I triangulations that typically appear at the centres of layered torus bundles. More...
class	TxIParallelCore
	A specific six-tetrahedron TxICore triangulation that does not fit neatly into other families. More...
class	TypeTrie
	A trie that stores a set of type vectors of a fixed length. More...
class	UnsolvedCase
	An exception thrown when a mathematical function is not able to solve a particular instance of a problem. More...
class	ValidityConstraints
	Represents a set of combinatorial validity constraints for use with polytope vertex enumeration. More...
class	Vector
	An optimised vector class of elements from a given ring T. More...
class	XMLTriangulationReader
class	XMLWriter

Typedefs
using	MatrixInt = Matrix<Integer, true>
	A matrix of arbitrary-precision integers.
using	AngleAlg = regina::Flags<AngleAlgFlags>
	A combination of flags for angle structure enumeration algorithms.
using	CensusPurge = regina::Flags<CensusPurgeFlags>
	A combination of flags for census generation.
using	HyperList = regina::Flags<HyperListFlags>
	A combination of flags for types of normal hypersurface lists.
using	HyperAlg = regina::Flags<HyperAlgFlags>
	A combination of flags for normal hypersurface enumeration algorithms.
using	LargeInteger = IntegerBase<true>
	LargeInteger is a type alias for IntegerBase<true>, which offers arbitrary precision integers with support for infinity.
using	Integer = IntegerBase<false>
	Integer is a type alias for IntegerBase<false>, which offers arbitrary precision integers without support for infinity.
using	NativeLong = NativeInteger<sizeof(long)>
	NativeLong is a type alias for the NativeInteger template class whose underlying integer type is a native long.
using	MatrixBool = Matrix<bool>
	A matrix of booleans.
using	VectorInt = Vector<Integer>
	A vector of arbitrary-precision integers.
using	VectorLarge = Vector<LargeInteger>
	A vector of arbitrary-precision integers that allows infinite elements.
template<typename T >
using	DiscSetSurfaceData = DiscSetSurfaceDataImpl<DiscSetTetData<T>>
	A structure that stores data of type T alongside every normal disc within a particular normal surface.
using	DiscSetSurface = DiscSetSurfaceDataImpl<DiscSetTet>
	A structure that builds all of the normal discs within a particular normal surface, but does not store any additional data alongside them.
using	NormalList = regina::Flags<NormalListFlags>
	A combination of flags for types of normal surface lists.
using	NormalAlg = regina::Flags<NormalAlgFlags>
	A combination of flags for normal surface enumeration algorithms.
using	SurfaceExport = regina::Flags<SurfaceExportFields>
	A set of fields to export alongside a normal surface list.
template<int dim>
using	Vertex = Face<dim, 0>
	Refers to a vertex of a dim-dimensional triangulation.
template<int dim>
using	Edge = Face<dim, 1>
	Refers to an edge of a dim-dimensional triangulation.
template<int dim>
using	Triangle = Face<dim, 2>
	Refers to a triangular face of a dim-dimensional triangulation.
template<int dim>
using	Tetrahedron = Face<dim, 3>
	Refers to a tetrahedral face of a dim-dimensional triangulation.
template<int dim>
using	Pentachoron = Face<dim, 4>
	Refers to a pentachoron face of a dim-dimensional triangulation.
template<int dim>
using	Simplex = Face<dim, dim>
	Refers to a top-dimensional simplex in a dim-dimensional triangulation.
template<int dim>
using	VertexEmbedding = FaceEmbedding<dim, 0>
	Details how a vertex of a dim-dimensional triangulation appears within each top-dimensional simplex.
template<int dim>
using	EdgeEmbedding = FaceEmbedding<dim, 1>
	Details how a edge of a dim-dimensional triangulation appears within each top-dimensional simplex.
template<int dim>
using	TriangleEmbedding = FaceEmbedding<dim, 2>
	Details how a triangular face of a dim-dimensional triangulation appears within each top-dimensional simplex.
template<int dim>
using	TetrahedronEmbedding = FaceEmbedding<dim, 3>
	Details how a tetrahedral face of a dim-dimensional triangulation appears within each top-dimensional simplex.
template<int dim>
using	PentachoronEmbedding = FaceEmbedding<dim, 4>
	Details how a pentachoron face of a dim-dimensional triangulation appears within each top-dimensional simplex.
template<int dim>
using	IsoSigEdgeDegrees = IsoSigDegrees<dim, 1>
	Defines an alternate type of isomorphism signature based on edge degree sequences.
template<int dim>
using	IsoSigRidgeDegrees = IsoSigDegrees<dim, dim - 2>
	Defines an alternate type of isomorphism signature based on degree sequences of (dim-2)-faces.
template<int pos, typename tuple , typename out_of_range = void>
using	safe_tuple_element
	An alternative to std::tuple_element that gracefully handles an out-of-range index.

Enumerations
enum	AngleAlgFlags {   AS_ALG_DEFAULT = 0x0000 , AS_ALG_TREE = 0x0010 , AS_ALG_DD = 0x0020 , AS_ALG_LEGACY = 0x4000 ,   AS_ALG_CUSTOM = 0x8000 }
	Represents options and variants of algorithms for enumerating various types of angle structures on 3-manifold triangulations. More...
enum	CensusPurgeFlags {   PURGE_NONE = 0x00 , PURGE_NON_MINIMAL = 0x01 , PURGE_NON_PRIME = 0x02 , PURGE_NON_MINIMAL_PRIME = 0x03 ,   PURGE_NON_MINIMAL_HYP = 0x09 , PURGE_P2_REDUCIBLE = 0x04 }
	Represents different classes of triangulations that may be ignored by census generation algorithms. More...
enum	FileFormat { REGINA_BINARY_GEN_1 = 1 , REGINA_XML_GEN_2 = 2 , REGINA_XML_GEN_3 = 3 , REGINA_CURRENT_FILE_FORMAT = REGINA_XML_GEN_3 }
	Represents each generation of Regina's file formats. More...
enum	HyperCoords { HS_STANDARD = 0 , HS_PRISM = 1 , HS_EDGE_WEIGHT = 200 }
	Represents different coordinate systems that can be used for enumerating and/or displaying normal hypersurfaces within 4-manifold triangulations. More...
enum	HyperListFlags {   HS_LIST_DEFAULT = 0x0000 , HS_EMBEDDED_ONLY = 0x0001 , HS_IMMERSED_SINGULAR = 0x0002 , HS_VERTEX = 0x0004 ,   HS_FUNDAMENTAL = 0x0008 , HS_LEGACY = 0x4000 , HS_CUSTOM = 0x8000 }
	Represents different lists of normal hypersurfaces that might be constructed for a given 4-manifold triangulation. More...
enum	HyperAlgFlags {   HS_ALG_DEFAULT = 0x0000 , HS_VERTEX_DD = 0x0020 , HS_HILBERT_PRIMAL = 0x0100 , HS_HILBERT_DUAL = 0x0200 ,   HS_ALG_LEGACY = 0x4000 , HS_ALG_CUSTOM = 0x8000 }
	Represents options and variants of algorithms for enumerating various types of normal hypersurfaces in 4-manifold triangulations. More...
enum	Framing { FRAMING_SEIFERT = 1 , FRAMING_BLACKBOARD = 2 }
	Indicates one of the standard framings of a knot or link. More...
enum	PermCodeType { PERM_CODE_IMAGES = 1 , PERM_CODE_INDEX = 2 }
	Represents the different kinds of internal permutation codes that are used in Regina's various Perm<n> template classes. More...
enum	NamedPermGroup { PERM_GROUP_TRIVIAL = 0 , PERM_GROUP_SYMMETRIC = 1 , PERM_GROUP_ALTERNATING = 2 }
	Constants that represent particular well-known classes of permutation groups. More...
enum	PacketHeldBy { HELD_BY_NONE = 0 , HELD_BY_PACKET = 1 , HELD_BY_SNAPPEA = 2 }
	Internal constants that support wrapped packets. More...
enum	PacketType {   PACKET_NONE = 0 , PACKET_CONTAINER = 1 , PACKET_TEXT = 2 , PACKET_NORMALSURFACES = 6 ,   PACKET_SCRIPT = 7 , PACKET_SURFACEFILTER = 8 , PACKET_ANGLESTRUCTURES = 9 , PACKET_ATTACHMENT = 10 ,   PACKET_NORMALHYPERSURFACES = 13 , PACKET_SNAPPEATRIANGULATION = 16 , PACKET_LINK = 17 , PACKET_TRIANGULATION2 = 15 ,   PACKET_TRIANGULATION3 = 3 , PACKET_TRIANGULATION4 = 11 , PACKET_TRIANGULATION5 = 105 , PACKET_TRIANGULATION6 = 106 ,   PACKET_TRIANGULATION7 = 107 , PACKET_TRIANGULATION8 = 108 }
	Represents the different types of packet that are available in Regina. More...
enum	Algorithm { ALG_DEFAULT = 0 , ALG_BACKTRACK = 1 , ALG_TREEWIDTH = 2 , ALG_NAIVE = 3 }
	Represents various classes of algorithms that Regina can use for computations. More...
enum	NormalCoords {   NS_STANDARD = 0 , NS_QUAD = 1 , NS_QUAD_CLOSED = 10 , NS_AN_LEGACY = 100 ,   NS_AN_QUAD_OCT = 101 , NS_AN_STANDARD = 102 , NS_AN_QUAD_OCT_CLOSED = 110 , NS_EDGE_WEIGHT = 200 ,   NS_TRIANGLE_ARCS = 201 , NS_ANGLE = 400 }
	Represents different coordinate systems that can be used for enumerating and/or displaying normal surfaces. More...
enum	NormalListFlags {   NS_LIST_DEFAULT = 0x0000 , NS_EMBEDDED_ONLY = 0x0001 , NS_IMMERSED_SINGULAR = 0x0002 , NS_VERTEX = 0x0004 ,   NS_FUNDAMENTAL = 0x0008 , NS_LEGACY = 0x4000 , NS_CUSTOM = 0x8000 }
	Represents different lists of normal surfaces that might be constructed for a given 3-manifold triangulation. More...
enum	NormalAlgFlags {   NS_ALG_DEFAULT = 0x0000 , NS_VERTEX_VIA_REDUCED = 0x0001 , NS_VERTEX_STD_DIRECT = 0x0002 , NS_VERTEX_TREE = 0x0010 ,   NS_VERTEX_DD = 0x0020 , NS_HILBERT_PRIMAL = 0x0100 , NS_HILBERT_DUAL = 0x0200 , NS_HILBERT_CD = 0x0400 ,   NS_HILBERT_FULLCONE = 0x0800 , NS_ALG_LEGACY = 0x4000 , NS_ALG_CUSTOM = 0x8000 }
	Represents options and variants of algorithms for enumerating various types of normal surfaces in 3-manifold triangulations. More...
enum	NormalTransform {   NS_CONV_REDUCED_TO_STD = 0x01 , NS_CONV_STD_TO_REDUCED = 0x02 , NS_FILTER_COMPATIBLE = 0x10 , NS_FILTER_DISJOINT = 0x20 ,   NS_FILTER_INCOMPRESSIBLE = 0x30 }
	Represents different ways in which Regina can transform one normal surface list into another. More...
enum	SurfaceExportFields {   surfaceExportName = 0x0001 , surfaceExportEuler = 0x0002 , surfaceExportOrient = 0x0004 , surfaceExportSides = 0x0008 ,   surfaceExportBdry = 0x0010 , surfaceExportLink = 0x0020 , surfaceExportType = 0x0040 , surfaceExportNone = 0 ,   surfaceExportAllButName = 0x007e , surfaceExportAll = 0x007f }
	Used to describe a field, or a set of fields, that can be exported alongside a normal surface list. More...
enum	SurfaceFilterType { NS_FILTER_LEGACY_DEFAULT = 0 , NS_FILTER_PROPERTIES = 1 , NS_FILTER_COMBINATION = 2 }
	Represents different types of filter classes that can be used to filter lists of normal surfaces in 3-manifold triangulations. More...
enum	TreeDecompositionAlg { TD_UPPER = 0x0001 , TD_UPPER_GREEDY_FILL_IN = 0x0001 }
	Indicates which algorithm should be used to compute a tree decomposition of a graph. More...
enum	BagComparison { BAG_EQUAL = 0 , BAG_SUBSET = -1 , BAG_SUPERSET = 1 , BAG_UNRELATED = 2 }
	Indicates the relationship between two bags in a tree decomposition. More...
enum	NiceType { NICE_INTRODUCE = 1 , NICE_FORGET = 2 , NICE_JOIN = 3 }
	Used to indicate the type of each bag in a nice tree decomposition. More...

Functions
void	swap (AbelianGroup &lhs, AbelianGroup &rhs) noexcept
	Swaps the contents of the two given abelian groups.
std::ostream &	operator<< (std::ostream &out, const GroupExpressionTerm &term)
	Writes the given term to the given output stream.
void	swap (GroupExpression &lhs, GroupExpression &rhs) noexcept
	Swaps the contents of the two given expressions.
void	swap (GroupPresentation &lhs, GroupPresentation &rhs) noexcept
	Swaps the contents of the two given group presentations.
void	swap (HomGroupPresentation &lhs, HomGroupPresentation &rhs) noexcept
	Swaps the contents of the two given homomorphisms.
void	swap (IntersectionForm &lhs, IntersectionForm &rhs) noexcept
	Swaps the contents of the two given intersection forms.
void	swap (MarkedAbelianGroup &lhs, MarkedAbelianGroup &rhs) noexcept
	Swaps the contents of the two given abelian groups.
void	swap (HomMarkedAbelianGroup &lhs, HomMarkedAbelianGroup &rhs) noexcept
	Swaps the contents of the two given homomorphisms.
AngleAlg	operator| (AngleAlgFlags lhs, AngleAlgFlags rhs)
	Returns the bitwise OR of the two given flags.
void	swap (AngleStructure &a, AngleStructure &b) noexcept
	Swaps the contents of the given angle structures.
void	swap (AngleStructures &lhs, AngleStructures &rhs)
	Swaps the contents of the two given lists.
MatrixInt	makeAngleEquations (const Triangulation< 3 > &tri)
	Generates the set of angle structure equations for the given triangulation.
void	swap (CensusDB &a, CensusDB &b) noexcept
	Swaps the contents of the given database references.
void	swap (CensusHit &a, CensusHit &b) noexcept
	Swaps the contents of the given census hits.
template<int dim>
void	swap (GluingPerms< dim > &a, GluingPerms< dim > &b) noexcept
	Swaps the contents of the given gluing permutation sets.
CensusPurge	operator| (CensusPurgeFlags lhs, CensusPurgeFlags rhs)
	Returns the bitwise OR of the two given flags.
const char *	versionString ()
	Returns the full version number of this calculation engine.
int	versionMajor ()
	Returns the major version number of this calculation engine.
int	versionMinor ()
	Returns the minor version number of this calculation engine.
const char *	buildInfo ()
	Returns any additional information about this specific build of Regina.
bool	versionUsesUTF8 (const char *version)
	Did the given version of Regina consistently use UTF-8 in its data files?
const char *	versionSnapPy ()
	Returns the version of SnapPy whose underlying SnapPea kernel is built into Regina.
const char *	versionSnapPea ()
	An alias for versionSnapPy(), which returns the version of SnapPy whose underlying SnapPea kernel is built into Regina.
int	versionPybind11Major ()
	Returns the major version of pybind11 that is used with Regina's python bindings.
bool	hasInt128 ()
	Does this particular build of Regina support native 128-bit arithmetic?
int	politeThreads ()
	A suggestion for user interfaces as to how many threads should be used for parallel computations.
int	testEngine (int value)
	Tests to see if an interface can successfully communicate with the underlying C++ calculation engine.
template<class T , bool supportsUtf8>
std::ostream &	operator<< (std::ostream &out, const Output< T, supportsUtf8 > &object)
	Writes the short text representation of the given object to the given output stream.
template<typename IntType >
void	swap (LPMatrix< IntType > &a, LPMatrix< IntType > &b) noexcept
	Swaps the contents of the given matrices.
template<typename IntType >
void	swap (LPInitialTableaux< IntType > &a, LPInitialTableaux< IntType > &b) noexcept
	Swaps the contents of the given matrices.
template<class LPConstraint , typename IntType >
void	swap (LPData< LPConstraint, IntType > &a, LPData< LPConstraint, IntType > &b) noexcept
	Swaps the contents of the given tableaux.
template<int nTypes>
void	swap (TypeTrie< nTypes > &a, TypeTrie< nTypes > &b) noexcept
	Swaps the contents of the two given tries.
void	swap (ValidityConstraints &a, ValidityConstraints &b) noexcept
	Swaps the contents of the two given constraint sets.
void	swap (FileInfo &a, FileInfo &b) noexcept
	Swaps the contents of the two given file information objects.
std::shared_ptr< Container >	readDehydrationList (const char *filename, unsigned colDehydrations=0, int colLabels=-1, unsigned long ignoreLines=0)
	Reads a list of dehydrated triangulations from the given text file.
template<class ObjectType >
std::shared_ptr< Container >	readSigList (const char *filename, unsigned colSigs=0, int colLabels=-1, unsigned long ignoreLines=0)
	Reads a list of isomorphism signatures or knot signatures from the given text file.
std::shared_ptr< PacketOf< Triangulation< 3 > > >	readOrb (const char *filename)
	Reads a triangulation from the given Orb / Casson file.
HyperList	operator| (HyperListFlags lhs, HyperListFlags rhs)
	Returns the bitwise OR of the two given flags.
HyperAlg	operator| (HyperAlgFlags lhs, HyperAlgFlags rhs)
	Returns the bitwise OR of the two given flags.
void	swap (NormalHypersurface &a, NormalHypersurface &b) noexcept
	Swaps the contents of the given normal hypersurfaces.
void	swap (NormalHypersurfaces &lhs, NormalHypersurfaces &rhs)
	Swaps the contents of the two given lists.
MatrixInt	makeMatchingEquations (const Triangulation< 4 > &triangulation, HyperCoords coords)
	Generates the set of normal hypersurface matching equations for the given triangulation using the given coordinate system.
ValidityConstraints	makeEmbeddedConstraints (const Triangulation< 4 > &triangulation, HyperCoords coords)
	Generates the validity constraints representing the condition that normal hypersurfaces be embedded.
std::ostream &	operator<< (std::ostream &out, const StrandRef &s)
	Writes a depiction of the given strand reference to the given output stream.
void	swap (Link &lhs, Link &rhs)
	Swaps the contents of the two given links.
std::ostream &	operator<< (std::ostream &out, const ModelLinkGraphArc &a)
	Writes a depiction of the given arc reference to the given output stream.
void	swap (ModelLinkGraph &lhs, ModelLinkGraph &rhs) noexcept
	Swaps the contents of the two given graphs.
void	swap (Tangle &lhs, Tangle &rhs) noexcept
	Swaps the contents of the two given tangles.
void	swap (GraphLoop &a, GraphLoop &b) noexcept
	Swaps the contents of the two given graph manifolds.
void	swap (GraphPair &a, GraphPair &b) noexcept
	Swaps the contents of the two given graph manifolds.
void	swap (GraphTriple &a, GraphTriple &b) noexcept
	Swaps the contents of the two given graph manifolds.
void	swap (Handlebody &a, Handlebody &b) noexcept
	Swaps the contents of the two given handlebodies.
void	swap (LensSpace &a, LensSpace &b) noexcept
	Swaps the contents of the two given lens spaces.
std::ostream &	operator<< (std::ostream &out, const SFSFibre &f)
	Writes the given fibre in human-readable format to the given output stream.
void	swap (SFSpace &a, SFSpace &b) noexcept
	Swaps the contents of the two given Seifert fibred spaces.
void	swap (SFSAlt &a, SFSAlt &b) noexcept
	Swaps the contents of the two given alternative representations of Seifert fibred spaces.
void	swap (SimpleSurfaceBundle &a, SimpleSurfaceBundle &b) noexcept
	Swaps the contents of the two given surface bundles.
void	swap (SnapPeaCensusManifold &a, SnapPeaCensusManifold &b) noexcept
	Swaps the contents of the two given SnapPea census manifolds.
void	swap (TorusBundle &a, TorusBundle &b) noexcept
	Swaps the contents of the two given torus bundles.
constexpr int	binomSmall (int n, int k)
	Returns the binomial coefficient n choose k in constant time for small arguments (n ≤ 16).
constexpr long	binomMedium (int n, int k)
	Returns the binomial coefficient n choose k in linear time for medium-sized arguments (n ≤ 29).
void	swap (Cyclotomic &a, Cyclotomic &b) noexcept
	Swaps the contents of the given field elements.
Cyclotomic	operator* (Cyclotomic elt, const Rational &scalar)
	Multiplies the given field element by the given rational.
Cyclotomic	operator* (const Rational &scalar, Cyclotomic elt)
	Multiplies the given field element by the given rational.
Cyclotomic	operator/ (Cyclotomic elt, const Rational &scalar)
	Divides the given field element by the given rational.
Cyclotomic	operator+ (const Cyclotomic &lhs, const Cyclotomic &rhs)
	Adds the two given cyclotomic field elements.
Cyclotomic	operator+ (Cyclotomic &&lhs, const Cyclotomic &rhs)
	Adds the two given cyclotomic field elements.
Cyclotomic	operator+ (const Cyclotomic &lhs, Cyclotomic &&rhs)
	Adds the two given cyclotomic field elements.
Cyclotomic	operator+ (Cyclotomic &&lhs, Cyclotomic &&rhs)
	Adds the two given cyclotomic field elements.
Cyclotomic	operator- (Cyclotomic arg)
	Returns the negative of the given field element.
Cyclotomic	operator- (const Cyclotomic &lhs, const Cyclotomic &rhs)
	Subtracts the two given cyclotomic field elements.
Cyclotomic	operator- (Cyclotomic &&lhs, const Cyclotomic &rhs)
	Subtracts the two given cyclotomic field elements.
Cyclotomic	operator- (const Cyclotomic &lhs, Cyclotomic &&rhs)
	Subtracts the two given cyclotomic field elements.
Cyclotomic	operator- (Cyclotomic &&lhs, Cyclotomic &&rhs)
	Subtracts the two given cyclotomic field elements.
Cyclotomic	operator* (const Cyclotomic &lhs, const Cyclotomic &rhs)
	Multiplies the two given cyclotomic field elements.
Cyclotomic	operator/ (const Cyclotomic &lhs, const Cyclotomic &rhs)
	Divides the two given cyclotomic field elements.
template<bool supportInfinity>
void	swap (IntegerBase< supportInfinity > &a, IntegerBase< supportInfinity > &b) noexcept
	Swaps the contents of the given integers.
template<bool supportInfinity>
std::ostream &	operator<< (std::ostream &out, const IntegerBase< supportInfinity > &i)
	Writes the given integer to the given output stream.
template<bool supportInfinity>
IntegerBase< supportInfinity >	operator+ (long lhs, const IntegerBase< supportInfinity > &rhs)
	Adds the given native integer to the given large integer.
template<bool supportInfinity>
IntegerBase< supportInfinity >	operator* (long lhs, const IntegerBase< supportInfinity > &rhs)
	Multiplies the given native integer with the given large integer.
template<bool supportInfinity>
void	tightEncode (std::ostream &out, IntegerBase< supportInfinity > value)
	Writes the tight encoding of the given arbitrary precision integer to the given output stream.
template<bool supportInfinity>
std::string	tightEncoding (IntegerBase< supportInfinity > value)
	Returns the tight encoding of the given arbitrary precision integer.
template<int bytes>
void	swap (NativeInteger< bytes > &a, NativeInteger< bytes > &b) noexcept
	Swaps the contents of the given integers.
template<int bytes>
std::ostream &	operator<< (std::ostream &out, const NativeInteger< bytes > &i)
	Writes the given integer to the given output stream.
template<typename T >
void	swap (Laurent< T > &a, Laurent< T > &b) noexcept
	Swaps the contents of the given polynomials.
template<typename T >
Laurent< T >	operator* (Laurent< T > poly, const typename Laurent< T >::Coefficient &scalar)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Laurent< T >	operator* (const typename Laurent< T >::Coefficient &scalar, Laurent< T > poly)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Laurent< T >	operator/ (Laurent< T > poly, const typename Laurent< T >::Coefficient &scalar)
	Divides the given polynomial by the given scalar constant.
template<typename T >
Laurent< T >	operator+ (const Laurent< T > &lhs, const Laurent< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Laurent< T >	operator+ (Laurent< T > &&lhs, const Laurent< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Laurent< T >	operator+ (const Laurent< T > &lhs, Laurent< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Laurent< T >	operator+ (Laurent< T > &&lhs, Laurent< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Laurent< T >	operator- (Laurent< T > arg)
	Returns the negative of the given polynomial.
template<typename T >
Laurent< T >	operator- (const Laurent< T > &lhs, const Laurent< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent< T >	operator- (Laurent< T > &&lhs, const Laurent< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent< T >	operator- (const Laurent< T > &lhs, Laurent< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent< T >	operator- (Laurent< T > &&lhs, Laurent< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent< T >	operator* (const Laurent< T > &lhs, const Laurent< T > &rhs)
	Multiplies the two given polynomials.
template<typename T >
void	swap (Laurent2< T > &a, Laurent2< T > &b) noexcept
	Swaps the contents of the given polynomials.
template<typename T >
Laurent2< T >	operator* (Laurent2< T > poly, const typename Laurent2< T >::Coefficient &scalar)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Laurent2< T >	operator* (const typename Laurent2< T >::Coefficient &scalar, Laurent2< T > poly)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Laurent2< T >	operator/ (Laurent2< T > poly, const typename Laurent2< T >::Coefficient &scalar)
	Divides the given polynomial by the given scalar constant.
template<typename T >
Laurent2< T >	operator+ (const Laurent2< T > &lhs, const Laurent2< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Laurent2< T >	operator+ (Laurent2< T > &&lhs, const Laurent2< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Laurent2< T >	operator+ (const Laurent2< T > &lhs, Laurent2< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Laurent2< T >	operator+ (Laurent2< T > &&lhs, Laurent2< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Laurent2< T >	operator- (Laurent2< T > arg)
	Returns the negative of the given polynomial.
template<typename T >
Laurent2< T >	operator- (const Laurent2< T > &lhs, const Laurent2< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent2< T >	operator- (Laurent2< T > &&lhs, const Laurent2< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent2< T >	operator- (const Laurent2< T > &lhs, Laurent2< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent2< T >	operator- (Laurent2< T > &&lhs, Laurent2< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Laurent2< T >	operator* (const Laurent2< T > &lhs, const Laurent2< T > &rhs)
	Multiplies the two given polynomials.
template<typename T >
void	swap (Matrix< T > &a, Matrix< T > &b) noexcept
	Swaps the contents of the given matrices.
void	swap (Matrix2 &a, Matrix2 &b) noexcept
	Swaps the contents of the two given matrices.
std::ostream &	operator<< (std::ostream &out, const Matrix2 &mat)
	Writes the given matrix to the given output stream.
bool	simpler (const Matrix2 &m1, const Matrix2 &m2)
	Determines whether the first given matrix is more aesthetically pleasing than the second.
bool	simpler (const Matrix2 &pair1first, const Matrix2 &pair1second, const Matrix2 &pair2first, const Matrix2 &pair2second)
	Determines whether the first given pair of matrices is more aesthetically pleasing than the second pair.
void	smithNormalForm (MatrixInt &matrix)
	Transforms the given integer matrix into Smith normal form.
void	smithNormalForm (MatrixInt &matrix, MatrixInt &rowSpaceBasis, MatrixInt &rowSpaceBasisInv, MatrixInt &colSpaceBasis, MatrixInt &colSpaceBasisInv)
	A Smith normal form algorithm that also returns change of basis matrices.
void	metricalSmithNormalForm (MatrixInt &matrix, MatrixInt &rowSpaceBasis, MatrixInt &rowSpaceBasisInv, MatrixInt &colSpaceBasis, MatrixInt &colSpaceBasisInv)
	An alternative Smith normal form algorithm that also returns change of basis matrices.
size_t	rowBasis (MatrixInt &matrix)
	Find a basis for the row space of the given matrix.
size_t	rowBasisAndOrthComp (MatrixInt &input, MatrixInt &complement)
	Finds a basis for the row space of the given matrix, as well as an "incremental" basis for its orthogonal complement.
void	columnEchelonForm (MatrixInt &M, MatrixInt &R, MatrixInt &Ri, const std::vector< size_t > &rowList)
	Transforms a given matrix into column echelon form with respect to a collection of rows.
MatrixInt	preImageOfLattice (const MatrixInt &hom, const std::vector< Integer > &sublattice)
	Given a homomorphism from Z^n to Z^k and a sublattice of Z^k, compute the preimage of this sublattice under this homomorphism.
MatrixInt	torsionAutInverse (const MatrixInt &input, const std::vector< Integer > &invF)
	Given an automorphism of an abelian group, this procedure computes the inverse automorphism.
long	reducedMod (long k, long modBase)
	Reduces k modulo modBase to give the smallest possible absolute value.
long	gcd (long a, long b)
	Deprecated routine that calculates the greatest common divisor of two signed integers.
std::tuple< long, long, long >	gcdWithCoeffs (long a, long b)
	Calculates the greatest common divisor of two given integers and finds the smallest coefficients with which these integers combine to give their gcd.
long	lcm (long a, long b)
	Deprecated routine that calculates the lowest common multiple of two signed integers.
unsigned long	modularInverse (unsigned long n, unsigned long k)
	Calculates the multiplicative inverse of one integer modulo another.
constexpr char	digit (int i)
	Returns the character used to express the integer i in a permutation.
constexpr int64_t	factorial (int n)
	Returns the factorial of n.
template<int n>
std::ostream &	operator<< (std::ostream &out, const Perm< n > &p)
	Writes a string representation of the given permutation to the given output stream.
template<int n>
std::ostream &	operator<< (std::ostream &out, const PermClass< n > &c)
	Writes a string representation of the given conjugacy class of permutations to the given output stream.
template<typename T >
void	swap (Polynomial< T > &a, Polynomial< T > &b) noexcept
	Swaps the contents of the given polynomials.
template<typename T >
Polynomial< T >	operator* (Polynomial< T > poly, const typename Polynomial< T >::Coefficient &scalar)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Polynomial< T >	operator* (const typename Polynomial< T >::Coefficient &scalar, Polynomial< T > poly)
	Multiplies the given polynomial by the given scalar constant.
template<typename T >
Polynomial< T >	operator/ (Polynomial< T > poly, const typename Polynomial< T >::Coefficient &scalar)
	Divides the given polynomial by the given scalar constant.
template<typename T >
Polynomial< T >	operator+ (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Polynomial< T >	operator+ (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
	Adds the two given polynomials.
template<typename T >
Polynomial< T >	operator+ (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Polynomial< T >	operator+ (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
	Adds the two given polynomials.
template<typename T >
Polynomial< T >	operator- (Polynomial< T > arg)
	Returns the negative of the given polynomial.
template<typename T >
Polynomial< T >	operator- (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Polynomial< T >	operator- (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
	Subtracts the two given polynomials.
template<typename T >
Polynomial< T >	operator- (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Polynomial< T >	operator- (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
	Subtracts the two given polynomials.
template<typename T >
Polynomial< T >	operator* (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
	Multiplies the two given polynomials.
template<typename T >
Polynomial< T >	operator/ (Polynomial< T > lhs, const Polynomial< T > &rhs)
	Divides the two given polynomials.
void	swap (Rational &a, Rational &b) noexcept
	Swaps the contents of the given rationals.
std::ostream &	operator<< (std::ostream &out, const Rational &rat)
	Writes the given rational to the given output stream.
template<typename T >
void	swap (Vector< T > &a, Vector< T > &b) noexcept
	Swaps the contents of the given vectors.
template<class T >
std::ostream &	operator<< (std::ostream &out, const Vector< T > &vector)
	Writes the given vector to the given output stream.
void	swap (Attachment &a, Attachment &b)
	Swaps the contents of the given attachment packets.
void	swap (Container &, Container &)
	Swap function for container packets that does nothing.
template<typename Held >
std::shared_ptr< PacketOf< Held > >	make_packet (Held &&src)
	Converts a temporary Held object into a new wrapped packet, without making a deep copy.
template<typename Held >
std::shared_ptr< PacketOf< Held > >	make_packet (Held &&src, const std::string &label)
	Converts a temporary Held object into a new wrapped packet, without making a deep copy.
template<typename Held , typename... Args>
std::shared_ptr< PacketOf< Held > >	make_packet (std::in_place_t, Args &&... args)
	Creates a new packet that wraps a Held object, passing the given arguments to the Held constructor.
template<typename Held >
std::shared_ptr< PacketOf< Held > >	make_packet ()
	Creates a new packet that wraps a default-constructed Held object.
template<typename Held >
Held &	static_packet_cast (Packet &p)
	Casts a reference from Packet to Held, assuming that the given packet is actually a PacketOf<Held>.
template<typename Held >
const Held &	static_packet_cast (const Packet &p)
	Casts a const reference from Packet to Held, assuming that the given packet is actually a PacketOf<Held>.
std::shared_ptr< Packet >	open (const char *filename)
	Reads a Regina data file, and returns the corresponding packet tree.
std::shared_ptr< Packet >	open (std::istream &in)
	Reads a Regina data file from the given input stream, and returns the corresponding packet tree.
bool	operator== (const Packet *packet, PacketShell shell)
	Identifies if the given shell refers to the given packet.
bool	operator!= (const Packet *packet, PacketShell shell)
	Identifies if the given shell does not refer to the given packet.
void	swap (Script &a, Script &b)
	Swaps the contents of the given script packets.
void	swap (Text &a, Text &b)
	Swaps the contents of the given text packets.
constexpr bool	standardDim (int dim)
	Indicates whether the given dimension is one of Regina's standard dimensions.
constexpr int	maxDim ()
	Indicates that largest dimension of triangulation that Regina can work with.
void	swap (SnapPeaTriangulation &lhs, SnapPeaTriangulation &rhs)
	Swaps the contents of the two given SnapPea triangulations.
void	swap (SigPartialIsomorphism &a, SigPartialIsomorphism &b) noexcept
	Swaps the contents of the given partial isomorphisms.
void	swap (Signature &a, Signature &b) noexcept
	Swaps the contents of the given signatures.
void	swap (AugTriSolidTorus &a, AugTriSolidTorus &b) noexcept
	Swaps the contents of the two given structures.
void	swap (BlockedSFS &a, BlockedSFS &b) noexcept
	Swaps the contents of the two given structures.
void	swap (BlockedSFSLoop &a, BlockedSFSLoop &b) noexcept
	Swaps the contents of the two given structures.
void	swap (BlockedSFSPair &a, BlockedSFSPair &b) noexcept
	Swaps the contents of the two given structures.
void	swap (BlockedSFSTriple &a, BlockedSFSTriple &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredChain &a, LayeredChain &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredChainPair &a, LayeredChainPair &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredLensSpace &a, LayeredLensSpace &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredLoop &a, LayeredLoop &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredSolidTorus &a, LayeredSolidTorus &b) noexcept
	Swaps the contents of the two given structures.
void	swap (LayeredTorusBundle &a, LayeredTorusBundle &b) noexcept
	Swaps the contents of the two given structures.
void	swap (PluggedTorusBundle &a, PluggedTorusBundle &b) noexcept
	Swaps the contents of the two given structures.
void	swap (PlugTriSolidTorus &a, PlugTriSolidTorus &b) noexcept
	Swaps the contents of the two given structures.
void	swap (SatBlockModel &a, SatBlockModel &b) noexcept
	Swaps the contents of the two given models.
void	swap (SatBlockSpec &a, SatBlockSpec &b) noexcept
	Swaps the contents of the two given structures.
void	swap (SatRegion &a, SatRegion &b) noexcept
	Swaps the contents of the two given regions.
void	swap (SnapPeaCensusTri &a, SnapPeaCensusTri &b) noexcept
	Swaps the contents of the two given structures.
void	swap (SnappedBall &a, SnappedBall &b) noexcept
	Swaps the contents of the two given structures.
void	swap (SpiralSolidTorus &a, SpiralSolidTorus &b) noexcept
	Swaps the contents of the two given structures.
void	swap (TriSolidTorus &a, TriSolidTorus &b) noexcept
	Swaps the contents of the two given structures.
void	swap (TrivialTri &a, TrivialTri &b) noexcept
	Swaps the contents of the two given structures.
void	swap (TxIDiagonalCore &lhs, TxIDiagonalCore &rhs)
	Swaps the contents of the two given T x I triangulations.
void	swap (TxIParallelCore &lhs, TxIParallelCore &rhs)
	Swaps the contents of the two given T x I triangulations.
std::ostream &	operator<< (std::ostream &out, const DiscSpec &spec)
	Writes the given disc specifier to the given output stream.
bool	numberDiscsAwayFromVertex (int discType, int vertex)
	Determines whether or not normal discs of the given type are numbered away from the given vertex.
bool	discOrientationFollowsEdge (int discType, int vertex, int edgeStart, int edgeEnd)
	Determines whether or not the natural boundary orientation of a normal disc of the given type follows the given directed normal arc.
template<class T >
void	swap (DiscSetTetData< T > &a, DiscSetTetData< T > &b) noexcept
	Swaps the contents of the two given disc sets.
template<class T >
void	swap (DiscSetSurfaceDataImpl< T > &a, DiscSetSurfaceDataImpl< T > &b) noexcept
	Swaps the contents of the two given disc sets.
std::ostream &	operator<< (std::ostream &out, const DiscType &type)
	Writes the given disc type to the given output stream.
NormalList	operator| (NormalListFlags lhs, NormalListFlags rhs)
	Returns the bitwise OR of the two given flags.
NormalAlg	operator| (NormalAlgFlags lhs, NormalAlgFlags rhs)
	Returns the bitwise OR of the two given flags.
void	swap (NormalSurface &a, NormalSurface &b) noexcept
	Swaps the contents of the given normal surfaces.
SurfaceExport	operator| (SurfaceExportFields lhs, SurfaceExportFields rhs)
	Returns the bitwise OR of the two given flags.
void	swap (NormalSurfaces &lhs, NormalSurfaces &rhs)
	Swaps the contents of the two given lists.
MatrixInt	makeMatchingEquations (const Triangulation< 3 > &triangulation, NormalCoords coords)
	Generates the set of normal surface matching equations for the given triangulation using the given coordinate system.
ValidityConstraints	makeEmbeddedConstraints (const Triangulation< 3 > &triangulation, NormalCoords coords)
	Generates the validity constraints representing the condition that normal surfaces be embedded.
std::ostream &	operator<< (std::ostream &out, const PrismSpec &spec)
	Writes the given prism specifier to the given output stream.
void	swap (SurfaceFilterCombination &a, SurfaceFilterCombination &b)
	Swaps the contents of the given combination filters.
void	swap (SurfaceFilterProperties &a, SurfaceFilterProperties &b)
	Swaps the contents of the given property-based filters.
void	swap (TreeDecomposition &a, TreeDecomposition &b) noexcept
	Swaps the contents of the two given tree decompositions.
void	swap (Cut &a, Cut &b) noexcept
	Swaps the contents of the given cuts.
template<int dim>
void	swap (FacetPairing< dim > &a, FacetPairing< dim > &b) noexcept
	Swaps the contents of the given facet pairings.
template<int dim>
void	swap (Triangulation< dim > &lhs, Triangulation< dim > &rhs)
	Swaps the contents of the two given triangulations.
void	swap (HomologicalData &a, HomologicalData &b) noexcept
	Swaps the contents of the two given HomologicalData objects.
Triangulation< 3 > &	static_triangulation3_cast (Packet &p)
	Casts a reference from Packet to Triangulation<3>, allowing for the packet to hold either a Triangulation<3> or a SnapPeaTriangulation.
const Triangulation< 3 > &	static_triangulation3_cast (const Packet &p)
	Casts a const reference from Packet to Triangulation<3>, allowing for the packet to hold either a Triangulation<3> or a SnapPeaTriangulation.
template<int dim>
constexpr int	faceOppositeEdge (int i, int j)
	Returns the (dim-2)-face number that is opposite the edge joining vertices i and j in a dim-dimensional simplex.
std::ostream &	operator<< (std::ostream &out, const FacePair &pair)
	Writes the given face pair to the given output stream.
template<int dim>
std::ostream &	operator<< (std::ostream &out, const FacetSpec< dim > &spec)
	Writes the given facet specifier to the given output stream.
template<int dim>
void	swap (Isomorphism< dim > &a, Isomorphism< dim > &b) noexcept
	Swaps the contents of the given isomorphisms.
size_t	base64Length (size_t bytes)
	Returns the number of base64 characters required to encode the given number of bytes.
bool	isBase64 (char ch)
	Determines whether the given character is a base64 printable character as used by the base64 routines in Regina.
void	base64Encode (const char *in, size_t inlen, char *out, size_t outlen)
	Encodes the given sequence of raw bytes in base64, and writes the results into a preallocated output buffer.
size_t	base64Encode (const char *in, size_t inlen, char **out)
	Encodes the given sequence of raw bytes in base64, and passes back a newly allocated array containing the results.
bool	base64Decode (const char *in, size_t inlen, char *out, size_t *outlen)
	Decodes the given sequence of base64 characters, and writes the resulting raw bytes into a preallocated output buffer.
bool	base64Decode (const char *in, size_t inlen, char **out, size_t *outlen)
	Decodes the given sequence of base64 characters, and passes back a newly allocated array containing the results.
void	swap (Bitmask &a, Bitmask &b) noexcept
	Swaps the contents of the two given bitmasks.
std::ostream &	operator<< (std::ostream &out, const Bitmask &mask)
	Writes the given bitmask to the given output stream as a sequence of zeroes and ones.
template<typename T >
std::ostream &	operator<< (std::ostream &out, const Bitmask1< T > &mask)
	Writes the given bitmask to the given output stream as a sequence of zeroes and ones.
template<typename T , typename U >
std::ostream &	operator<< (std::ostream &out, const Bitmask2< T, U > &mask)
	Writes the given bitmask to the given output stream as a sequence of zeroes and ones.
std::ostream &	operator<< (std::ostream &out, BoolSet set)
	Writes the given boolean set to the given output stream.
template<typename IntType >
constexpr int	bitsRequired (IntType n)
	Returns the number of bits required to store integers in the range 0,...,n-1.
template<typename IntType >
constexpr IntType	nextPowerOfTwo (IntType n)
	Returns the smallest integer power of two that is greater than or equal to the given argument n.
template<typename T >
void	swap (MarkedVector< T > &a, MarkedVector< T > &b) noexcept
	Swaps the contents of the given vectors.
std::tuple< unsigned long, unsigned long, unsigned long >	resUsage ()
	Returns time and memory usage for the current process, for use on Linux systems.
void	writeResUsage (std::ostream &out)
	Writes time and memory usage for the current process to the given output stream, for use on Linux systems.
template<typename T >
std::ostream &	operator<< (std::ostream &out, const Qitmask1< T > &mask)
	Writes the given qitmask to the given output stream as a sequence of digits (0, 1, 2 and/or 3).
template<typename T , typename U >
std::ostream &	operator<< (std::ostream &out, const Qitmask2< T, U > &mask)
	Writes the given qitmask to the given output stream as a sequence of digits (0, 1, 2 and/or 3).
template<typename T >
std::ostream &	operator<< (std::ostream &out, const LightweightSequence< T > &s)
	Writes the given sequence to the given output stream.
template<typename T >
void	swap (LightweightSequence< T > &a, LightweightSequence< T > &b) noexcept
	Swaps the contents of the given sequences.
template<class T >
void	swap (SnapshotRef< T > &a, SnapshotRef< T > &b) noexcept
	Swaps the given references so that they refer to each others' snapshots.
bool	startsWith (const std::string &str, const std::string &prefix)
	Determines whether the given C++ string begins with the given prefix.
std::string	stripWhitespace (const std::string &str)
	Strips all whitespace from the beginning and end of the given C++ string.
bool	valueOf (const std::string &str, int8_t &dest)
	Converts the entire given string to an 8-bit integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, uint8_t &dest)
	Converts the entire given string to an unsigned 8-bit integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, short &dest)
	Converts the entire given string to a short integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, unsigned short &dest)
	Converts the entire given string to an unsigned short integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, int &dest)
	Converts the entire given string to an integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, unsigned &dest)
	Converts the entire given string to an unsigned integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, long &dest)
	Converts the entire given string to a long integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, unsigned long &dest)
	Converts the entire given string to an unsigned long integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, long long &dest)
	Converts the entire given string to a long long integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, unsigned long long &dest)
	Converts the entire given string to an unsigned long long integer and reports whether this conversion was successful.
bool	valueOf (const std::string &str, double &dest)
	Converts the entire given string to a double precision real number and reports whether this conversion was successful.
bool	valueOf (const std::string &str, bool &dest)
	Converts the entire given string to a boolean and reports whether this conversion was successful.
bool	valueOf (const std::string &str, BoolSet &dest)
	Converts the entire given string to a set of booleans and reports whether this conversion was successful.
std::vector< std::string >	basicTokenise (const std::string &str)
	Decomposes the given string into tokens.
std::string	stringToToken (std::string str)
	Returns a token derived from the given string.
template<typename T >
std::string	superscript (T value)
	Converts the given C++ integer into a unicode superscript string.
template<typename T >
std::string	subscript (T value)
	Converts the given C++ integer into a unicode subscript string.
void	tightEncode (std::ostream &out, int value)
	Writes the tight encoding of the given signed integer to the given output stream.
std::string	tightEncoding (int value)
	Returns the tight encoding of the given signed integer.
void	tightEncode (std::ostream &out, long value)
	Writes the tight encoding of the given signed long integer to the given output stream.
std::string	tightEncoding (long value)
	Returns the tight encoding of the given signed long integer.
void	tightEncode (std::ostream &out, long long value)
	Writes the tight encoding of the given signed long long integer to the given output stream.
std::string	tightEncoding (long long value)
	Returns the tight encoding of the given signed long long integer.
void	tightEncode (std::ostream &out, unsigned value)
	Writes the tight encoding of the given unsigned integer to the given output stream.
std::string	tightEncoding (unsigned value)
	Returns the tight encoding of the given unsigned integer.
void	tightEncode (std::ostream &out, unsigned long value)
	Writes the tight encoding of the given unsigned long integer to the given output stream.
std::string	tightEncoding (unsigned long value)
	Returns the tight encoding of the given unsigned long integer.
void	tightEncode (std::ostream &out, unsigned long long value)
	Writes the tight encoding of the given unsigned long long integer to the given output stream.
std::string	tightEncoding (unsigned long long value)
	Returns the tight encoding of the given unsigned long long integer.
void	tightEncode (std::ostream &out, bool value)
	Writes the tight encoding of the given boolean to the given output stream.
std::string	tightEncoding (bool value)
	Returns the tight encoding of the given boolean.
template<typename Int >
Int	tightDecoding (const std::string &enc)
	Reconstructs an integer or boolean from its given tight encoding.
template<typename Int >
Int	tightDecode (std::istream &input)
	Reconstructs an integer or boolean from its given tight encoding.
void	swap (TrieSet &a, TrieSet &b) noexcept
	Swaps the contents of the two given collections.
template<int from, int to, class Action >
constexpr void	for_constexpr (Action &&action)
	Implements a compile-time for loop over a range of integers.
template<int from, int to, typename Return , class Action >
constexpr Return	select_constexpr (int value, Action &&action)
	Implements a compile-time selection, where the runtime argument must belong to a compile-time range of integers, and the value of the argument determines what is returned.
template<int from, int to, class Action >
constexpr auto	select_constexpr_as_variant (int value, Action &&action)
	A variant of select_constexpr() where the return type is a variant, built from the return types for all integers in the given compile-time range.
const char *	pythonTypename (const std::type_info *t)
	Returns the preferred Python display name for the given C++ type.

Variables
template<typename Held >
static constexpr PacketType	packetTypeHolds = PACKET_NONE
	The packet type constant for a packet wrapping an object of type Held.
constexpr int	quadSeparating [4][4]
	Lists which quadrilateral types separate which pairs of vertices in a tetrahedron.
constexpr int	quadMeeting [4][4][2]
	Lists which quadrilateral types meet which edges in a tetrahedron.
constexpr int	quadDefn [3][4]
	Lists which vertices each quadrilateral type separates in a tetrahedron.
constexpr int	quadPartner [3][4]
	Lists the second vertex with which each vertex is paired under each quadrilateral type in a tetrahedron.
const std::string	quadString [3] = { "01/23", "02/13", "03/12" }
	Contains strings that can be used to represent each quadrilateral type in a tetrahedron.
constexpr Perm< 4 >	triDiscArcs [4][3]
	Lists in consecutive order the directed normal arcs that form the boundary of each type of triangular normal disc.
constexpr Perm< 4 >	quadDiscArcs [3][4]
	Lists in consecutive order the directed normal arcs that form the boundary of each type of quadrilateral normal disc.
constexpr Perm< 4 >	octDiscArcs [3][8]
	Lists in consecutive order the directed normal arcs that form the boundary of each type of octagonal normal disc.
constexpr char	base64Table []
	The table of all base64 printable characters, as used by the base64 routines in Regina.
constexpr char	base64Spare [] = "_-."
	A table of printable characters that are not amongst the base64 printable characters used by Regina.
template<typename IntType , IntType coeff>
constexpr IntType	maxSafeFactor
	The largest integer of the given type that can be multiplied by coeff without overflowing.
template<typename IntType , IntType coeff>
constexpr IntType	minSafeFactor
	The largest integer of the given type that can be multiplied by coeff without overflowing.

Detailed Description

Contains the entire Regina calculation engine.

Define REGINA_VERIFY_LPDATA to check invariants as the algorithm runs.

This checking is slow and can increase the running time significantly.

Typedef Documentation

safe_tuple_element

template<int pos, typename tuple , typename out_of_range = void>

using regina::safe_tuple_element

Initial value:

 typename regina::detail::safe_tuple_element_impl<
    pos, tuple, out_of_range>::type

An alternative to std::tuple_element that gracefully handles an out-of-range index.

If pos is a valid index into the tuple type tuple, then this type alias is identical to std::tuple_element<pos, tuple>::type. Otherwise this type alias is identical to the argument out_of_range.

Note that you should not append type when using safe_tuple_element (i.e., this is really a drop-in replacement for the C++17 type alias std::tuple_element_t, and not the C++11 structure std::tuple_element).

Template Parameters

pos	an index, which may take any integer value.
tuple	a std::tuple type (which is allowed to include const and/or volatile modifiers).
out_of_range	the type to use if pos is not a valid index into tuple.

Enumeration Type Documentation

NamedPermGroup

enum regina::NamedPermGroup

Constants that represent particular well-known classes of permutation groups.

These constants are intended to be used with permutation groups on n elements for arbitrary n. (In particular, you can pass them to the PermGroup<n> constructor.)

Enumerator
PERM_GROUP_TRIVIAL	Represents the trivial group on n elements, containing only the identity permutation.
PERM_GROUP_SYMMETRIC	Represents the symmetric group on n elements, containing all n! possible permutations.
PERM_GROUP_ALTERNATING	Represents the alternating group on n elements, containing all n!/2 even permutations.

PacketHeldBy

enum regina::PacketHeldBy

Internal constants that support wrapped packets.

These constants indicate whether an object of type Held is in fact part of the inherited interface for a derived class of Held, which is typically the wrapped packet type PacketOf<Held>. These constants are used as a lightweight (and significantly less rich) replacement for polymorphism, virtual functions and dynamic casts.

These constants only know about two types of relationships:

• an object of type Held being part of a larger PacketOf<Held> (indicated by the constant HELD_BY_PACKET);
• an object of type Triangulation<3> being part of a larger SnapPeaTriangulation (indicated by the constant HELD_BY_SNAPPEA).

Of course, a Triangulation<3> could belong to a SnapPeaTriangulation which is then held by a PacketOf<SnapPeaTriangulation>. In this case the inherited PacketData<Triangulation<3>> will store HELD_BY_SNAPPEA, and the inherited PacketData<SnapPeaTriangulation> will store HELD_BY_PACKET.

Python

Not present.

Enumerator
HELD_BY_NONE	Indicates that the object is not held within either a wrapped packet or a SnapPea triangulation.
HELD_BY_PACKET	Indicates that an object of type Held is in fact the inherited data for a PacketOf<Held>.
HELD_BY_SNAPPEA	Indicates that a Triangulation<3> is in fact the inherited native Regina data for a SnapPeaTriangulation.

Function Documentation

pythonTypename()

const char * regina::pythonTypename

(

const std::type_info *

t

)

Returns the preferred Python display name for the given C++ type.

The Python bindings have an internal mechanism for converting any C++ type into a suitable display name. However, for some of Regina's classes the results are not ideal.

For example, the 3-D triangulation class may be displayed as regina::Triangulation<3> instead of its "real" Python name regina.Triangulation3. (This kind of problem most commonly appears in docstrings, where function signatures are generated as each function is bound, which may happen before all of the types in the argument/return list have been bound.)

The purpose of this function is to override this default typename conversion mechanism. If the C++ type referred to by t has a known Python name that should always be used, this function will return it. Otherwise this function returns nullptr, indicating that the default conversion mechanism should be used.

Python

Not present.

Parameters

t	an object that references the C++ type whose display name we wish to obtain.

Returns

the preferred display name for this type in Python, or nullptr if the default C++-to-Python name conversion mechanism should be used.

tightDecode()

template<typename Int >

Int regina::tightDecode ( std::istream & input )

inline

Reconstructs an integer or boolean from its given tight encoding.

See the page on tight encodings for details.

The tight encoding will be read from the given input stream. If the input stream contains leading whitespace then it will be treated as an invalid encoding (i.e., this routine will throw an exception). The input routine may contain further data: if this routine is successful then the input stream will be left positioned immediately after the encoding, without skipping any trailing whitespace.

This routine does recognise infinity in the case where Int is the type regina::LargeInteger.

If Int is one of Regina's arbitrary precision integer types, then this routine is identical to calling Int::tightDecode().

Headers

Some components of this routine are implemented in a separate header (tightencoding-impl.h), which is not included automatically by this file. Most end users should not need this extra header, since Regina's calculation engine already includes explicit instantiations for all of the types that have corresponding global tightEncode() functions (i.e., bool; signed and unsigned int, long, and long long; and regina::Integer and regina::LargeInteger).

Exceptions

InvalidInput

The given input stream does not begin with a tight encoding of an integer/boolean of type Int. This includes the case where the encoding is a valid integer encoding but the integer itself is outside the allowed range for the Int type.

Python

Not present. Use regina::tightDecoding() instead, which takes a string as its argument.

Template Parameters

Int	The type of integer/boolean to reconstruct; this must be either (i) a native C++ integer type or bool, or (ii) one of Regina's arbitrary precision integer types (i.e., regina::Integer or regina::LargeInteger).

Parameters

input

an input stream that begins with the tight encoding for an integer or boolean.

Returns

the integer or boolean represented by the given tight encoding.

tightDecoding()

template<typename Int >

Int regina::tightDecoding ( const std::string & enc )

inline

Reconstructs an integer or boolean from its given tight encoding.

See the page on tight encodings for details.

The tight encoding should be given as a string. If this string contains leading whitespace or any trailing characters at all (including trailing whitespace), then it will be treated as an invalid encoding (i.e., this routine will throw an exception).

This routine does recognise infinity in the case where Int is the type regina::LargeInteger.

If Int is one of Regina's arbitrary precision integer types, then this routine is identical to calling Int::tightDecoding().

Headers

Some components of this routine are implemented in a separate header (tightencoding-impl.h), which is not included automatically by this file. Most end users should not need this extra header, since Regina's calculation engine already includes explicit instantiations for all of the types that have corresponding global tightEncode() functions (i.e., bool; signed and unsigned int, long, and long long; and regina::Integer and regina::LargeInteger).

Exceptions

InvalidArgument

The given string is not a tight encoding of an integer/boolean of type Int. This includes the case where the encoding is a valid integer encoding but the integer itself is outside the allowed range for the Int type.

Python

Since Python does not support templates, the interface for this routine is a little different. The global routine regina::tightDecoding() will return a Python integer; since these are arbitrary precision, the decoding will never encounter an out-of-range exceptions as it might with a native C++ integer type. If you are trying to reconstruct a boolean, then the integer you receive will be either 1 or 0 to represent true or false respectively. If you are trying to reconstruct one of Regina's arbitrary precision integer types, you should instead call Integer::tightDecoding() or LargeInteger::tightDecoding(), which will return a Regina integer instead of a Python integer.

Template Parameters

Int	The type of integer/boolean to reconstruct; this must be either (i) a native C++ integer type or bool, or (ii) one of Regina's arbitrary precision integer types (i.e., regina::Integer or regina::LargeInteger).

Parameters

enc	the tight encoding for an integer or boolean.

Returns

the integer or boolean represented by the given tight encoding.

versionPybind11Major()

int regina::versionPybind11Major

(

)

Returns the major version of pybind11 that is used with Regina's python bindings.

Currently this will return either 2 or 3 (according to whether you are building against Python ≤ 3.11 or Python ≥ 3.12 respectively).

C++

Not present.

Returns

the major pybind11 version.

writeResUsage()

void regina::writeResUsage

(

std::ostream &

out

)

Writes time and memory usage for the current process to the given output stream, for use on Linux systems.

This simply writes the information gathered from resUsage() to the given output stream in a human-readable format. See resUsage() for full details on what this information means and on what systems it can be accessed.

The output will be written in the following format, with no final newline, and without flushing the output stream:

utime=..., stime=..., vsize=...

Unline resUsage(), if an error occurs then this routine will not throw an exception. Instead it will write an appropriate message to the output stream.

Python

Not present. Instead use the variant resUsage() that takes no arguments and returns a tuple.

Parameters

out	the output stream to which to write.

Variable Documentation

packetTypeHolds

template<typename Held >

PacketType regina::packetTypeHolds = PACKET_NONE

staticconstexpr

The packet type constant for a packet wrapping an object of type Held.

This variable is only meaningful when Held is not itself a packet type, but instead is a standalone type that can (if desired) be wrapped in a packet of type PacketOf<Held>. Examples of such types include Link and Triangulation<dim>.

In all other cases, this variable will be PACKET_NONE.

In particular, if Held is a full packet type itself (such as Container, Script, or PacketOf<...>), then this template variable will be PACKET_NONE.

Python

Not present.