atlas::weyl::WeylElt Class Reference

Element of a Weyl group. More...

#include <weyl.h>

Inheritance diagram for atlas::weyl::WeylElt:

Public Types
typedef unsigned char	EltPiece
	Represents a minimal length coset representative for one of the parabolic subquotients W_{i-1}\W_i. More...

Public Member Functions
	WeylElt ()
	Constructs the identity element of W. More...
	WeylElt (const WeylWord &w, const WeylGroup &W)
	interpret |w| in weyl group |W| More...
bool	operator< (const WeylElt &w) const
	Tests whether this Weyl group element is lexicographically strictly less than the Weyl group element following the < sign. More...
bool	operator== (const WeylElt &w) const
	Tests whether this Weyl group element is equal to the Weyl group element following the == sign. More...
bool	operator!= (const WeylElt &w) const
	Tests whether this Weyl group element is not equal to the Weyl group element following the != sign. More...
const WeylElt &	w () const
WeylElt &	contents ()

Protected Member Functions
EltPiece	operator[] (size_t j) const
	Returns the jth factor of the Weyl group element. More...
EltPiece &	operator[] (size_t j)

Private Attributes
EltPiece	d_data [constants::RANK_MAX]
	Represents factorization of Weyl group element w as a product of shortest length coset representatives for parabolic subquotients W_{i-1}\W_i. More...

Friends
class	WeylGroup

Detailed Description

Element of a Weyl group.

The representation is described in detail in the description of the class WeylGroup. An array of RANK_MAX unsigned char, the ith representing a shortest length coset representative of a parabolic subquotient W_{i-1}\W_i.

Member Typedef Documentation

typedef unsigned char atlas::weyl::WeylElt::EltPiece

Represents a minimal length coset representative for one of the parabolic subquotients W_{i-1}\W_i.

Constructor & Destructor Documentation

atlas::weyl::WeylElt::WeylElt ( )

inline

Constructs the identity element of W.

atlas::weyl::WeylElt::WeylElt	(	const WeylWord &	w,
		const WeylGroup &	W
	)

interpret |w| in weyl group |W|

Member Function Documentation

WeylElt& atlas::weyl::WeylElt::contents ( )

inline

bool atlas::weyl::WeylElt::operator!= ( const WeylElt &  w ) const

inline

Tests whether this Weyl group element is not equal to the Weyl group element following the != sign.

bool atlas::weyl::WeylElt::operator< ( const WeylElt &  w ) const

inline

Tests whether this Weyl group element is lexicographically strictly less than the Weyl group element following the < sign.

bool atlas::weyl::WeylElt::operator== ( const WeylElt &  w ) const

inline

Tests whether this Weyl group element is equal to the Weyl group element following the == sign.

EltPiece atlas::weyl::WeylElt::operator[] ( size_t  j ) const

inlineprotected

Returns the jth factor of the Weyl group element.

EltPiece& atlas::weyl::WeylElt::operator[] ( size_t  j )

inlineprotected

const WeylElt& atlas::weyl::WeylElt::w ( ) const

inline

Friends And Related Function Documentation

friend class WeylGroup

friend

Member Data Documentation

EltPiece atlas::weyl::WeylElt::d_data[constants::RANK_MAX]

private

Represents factorization of Weyl group element w as a product of shortest length coset representatives for parabolic subquotients W_{i-1}\W_i.

Entry #i-1 is an unsigned char parametrizing the ith coset representative w_i for an element of W_{i-1}\W_i. Then w = w_1.w_2...w_n.

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

• /home/ran/atlas_project/latest_branch_07182016/sources/structure/weyl.h
• /home/ran/atlas_project/latest_branch_07182016/sources/structure/weyl.cpp