The Multiplication Graph created from the Multiplication Table. More...

#include <Mult_Graph.hpp>

Inheritance diagram for MultGraph< group_t >:

Collaboration diagram for MultGraph< group_t >:

Public Types
typedef Graph< Neighborhood< size_t, bicolored_edge_with_id, std::vector > >	graph_t

Public Member Functions
std::vector< int >	getdegree (int i) const
	Retrieve the degree of the i-th generator. More...

Eigen::Matrix< int, 1, -1 >	getelement (int i) const
	Retrieve the element the i-th generator corresponds to. More...

int	getelementindex (const std::vector< int > &deg, const rank_t &elmnt) const
	Retrieve the element index of the given degree and element. Returns -1 if no such degree can be found. More...

Public Member Functions inherited from Mult_Table< group_t >
	Mult_Table ()=default
	Default constructor. More...

	Mult_Table (int, const std::vector< int > &, const std::vector< int > &, const std::vector< std::vector< int >> &)
	Constructs the multiplication table given the maximum and minimum spheres and the basic irreducibles. More...

int	getdegreeindex (const std::vector< int > &) const
	Retrieve the degree index of the given degree. Returns -1 if no such degree can be found. More...

Public Attributes
int	number_of_generators
	The number of generators in the multiplication graph. More...

graph_t	graph

Protected Member Functions
	MultGraph (int, const std::vector< int > &, const std::vector< int > &, const std::vector< std::vector< int >> &)
	Constructs the multiplication graph given the maximum and minimum spheres and the basic irreducibles. More...

int	isMultiple (int i, int j) const
	Returns k if element[i]=k*element[j]. Returns 0 if element[a] is not a multiple of element[b]. More...

	MultGraph (Mult_Table< group_t > &)
	Constructs the multiplication graph given the multiplication table. More...

Protected Member Functions inherited from Mult_Table< group_t >
std::vector< int >	getsphere (const std::vector< int > &deg)
	Isolate sphere from the degree vector (i.e. get everything but first entry) More...

Green< group_t >	triple_product (int, int, int)
	Multiplies the given index with two basic irreducibles. Only used by Mult_Graph_Identify when all other identification techniques fail. More...

Protected Attributes
std::vector< rank_t >	element
	An element (linear combination of generators) in each NonZeroHomology group of the table. More...

std::vector< int >	tracker
	Maps element index to degree index. More...

std::map< std::pair< int, rank_t >, int, implementation_details::compareElements >	antielement
	Maps (degree_index, element)->element_index. The comparator first compares the degree_index and if equal then compares the elements first to last entry. More...

Protected Attributes inherited from Mult_Table< group_t >
int	level
	The Mackey functor level we are working in. More...

std::map< std::vector< int >, IDGenerators< rank_t > >	NonZeroHomology

std::vector< std::vector< int > >	degree
	Maps each index of NonZeroHomology to the corresponding degree. More...

std::map< std::vector< int >, int >	antidegree
	Maps each degree to the corresponding index of NonZeroHomology. More...

Eigen::Matrix< int, -1, -1 >	index_product
	Maps each index and irreducible to the index of their product. More...

std::vector< int >	minsphere
	The lower bound on the range of our spheres. More...

std::vector< int >	maxsphere
	The upper bound on the range of our spheres. More...

std::vector< std::vector< int > >	basicIrreducibles
	The basic irreducibles we use to produce the factorizations (eg Euler and orientation classes) More...

std::vector< std::vector< Green< group_t > > >	Greens
	Each entry in the multiplication table. More...

std::map< std::array< int, 3 >, Green< group_t > >	tripleGreens
	The tripleGreens set and used by Mult_Graph_Identify when all other identification techniques fail. More...

Friends
template<typename >
class	Mult_Graph_Identify

template<typename >
class	Mult_Graph_Connectivity

Detailed Description

template<typename group_t>
class Mackey::MultGraph< group_t >

The Multiplication Graph created from the Multiplication Table.

A node is an element in a nonzero homology group, a linear combination of the generators. At initialization we only use generators, but as products of generators might not be generators, after that initial stage we add multiples and linear combinations into the mix. We have a new index for the elements, and use various vectors and ordered maps to keep track of the element index and the degree index.

Member Typedef Documentation

◆ graph_t

typedef Graph<Neighborhood<size_t, bicolored_edge_with_id, std::vector> > graph_t

Constructor & Destructor Documentation

◆ MultGraph() [1/2]

MultGraph	(	int	,
		const std::vector< int > &	,
		const std::vector< int > &	,
		const std::vector< std::vector< int >> &
	)

protected

Constructs the multiplication graph given the maximum and minimum spheres and the basic irreducibles.

◆ MultGraph() [2/2]

MultGraph ( Mult_Table< group_t > & )

protected

Constructs the multiplication graph given the multiplication table.

Member Function Documentation

◆ getdegree()

std::vector<int> getdegree ( int i ) const

Retrieve the degree of the i-th generator.

◆ getelement()

Eigen::Matrix<int, 1, -1> getelement ( int i ) const

Retrieve the element the i-th generator corresponds to.

◆ getelementindex()

int getelementindex	(	const std::vector< int > &	deg,
		const rank_t &	elmnt
	)		const

Retrieve the element index of the given degree and element. Returns -1 if no such degree can be found.

◆ isMultiple()

int isMultiple	(	int	i,
		int	j
	)		const

protected

Returns k if element[i]=k*element[j]. Returns 0 if element[a] is not a multiple of element[b].

Friends And Related Function Documentation

◆ Mult_Graph_Identify

friend class Mult_Graph_Identify

friend

◆ Mult_Graph_Connectivity

friend class Mult_Graph_Connectivity

friend

Member Data Documentation

◆ number_of_generators

int number_of_generators

The number of generators in the multiplication graph.

◆ graph

graph_t graph

◆ element

std::vector<rank_t> element

protected

An element (linear combination of generators) in each NonZeroHomology group of the table.

◆ tracker

std::vector<int> tracker

protected

Maps element index to degree index.

◆ antielement

std::map<std::pair<int, rank_t>, int, implementation_details::compareElements> antielement

protected

Maps (degree_index, element)->element_index. The comparator first compares the degree_index and if equal then compares the elements first to last entry.

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

Mult_Graph.hpp

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<typename group_t> class Mackey::MultGraph< group_t >

Member Typedef Documentation

◆ graph_t

Constructor & Destructor Documentation

◆ MultGraph() [1/2]

◆ MultGraph() [2/2]

Member Function Documentation

◆ getdegree()

◆ getelement()

◆ getelementindex()

◆ isMultiple()

Friends And Related Function Documentation

◆ Mult_Graph_Identify

◆ Mult_Graph_Connectivity

Member Data Documentation

◆ number_of_generators

◆ graph

◆ element

◆ tracker

◆ antielement

template<typename group_t>
class Mackey::MultGraph< group_t >