atlas::weyl::WeylElt Class Reference

Element of a Weyl group. More...

#include <weyl.h>

Inheritance diagram for atlas::weyl::WeylElt:

[legend]List of all members.

Public Member Functions
	WeylElt ()
	Constructs the identity element of W.
	WeylElt (const WeylWord &w, const WeylGroup &W)
	interpret |w| in weyl group |W|
	WeylElt (const WeylElt &w)
WeylElt &	operator= (const WeylElt &w)
bool	operator< (const WeylElt &w) const
	Tests whether this Weyl group element is lexicographically strictly less than the Weyl group element following the < sign.
bool	operator== (const WeylElt &w) const
	Tests whether this Weyl group element is equal to the Weyl group element following the == sign.
bool	operator!= (const WeylElt &w) const
	Tests whether this Weyl group element is not equal to the Weyl group element following the != sign.
const WeylElt &	w () const
WeylElt &	contents ()
Protected Member Functions
EltPiece	operator[] (size_t j) const
	Returns the jth factor of the Weyl group element.
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.
Friends
class	WeylGroup

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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.

Definition at line 79 of file weyl.h.

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Constructor & Destructor Documentation

atlas::weyl::WeylElt::WeylElt (   )  [inline]

Constructs the identity element of W. Definition at line 104 of file weyl.h.

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

interpret |w| in weyl group |W| Definition at line 754 of file weyl.cpp. References d_data, and atlas::weyl::WeylGroup::mult().

atlas::weyl::WeylElt::WeylElt (  const WeylElt &  w  )  [inline]

Definition at line 112 of file weyl.h. References d_data.

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Member Function Documentation

WeylElt& atlas::weyl::WeylElt::contents (   )  [inline]

Definition at line 170 of file weyl.h. Referenced by atlas::weyl::WeylGroup::twistedConjugate().

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. Definition at line 144 of file weyl.h. References d_data.

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. Definition at line 128 of file weyl.h. References d_data.

WeylElt& atlas::weyl::WeylElt::operator= (  const WeylElt &  w  )  [inline]

Definition at line 116 of file weyl.h. References d_data.

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. Definition at line 136 of file weyl.h. References d_data.

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

Definition at line 158 of file weyl.h. References atlas::weyl::EltPiece.

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

Returns the jth factor of the Weyl group element. Definition at line 153 of file weyl.h. References atlas::weyl::EltPiece.

const WeylElt& atlas::weyl::WeylElt::w (   )  const [inline]

Definition at line 169 of file weyl.h. Referenced by atlas::kltest::checkBasePoint(), atlas::involutions::helper::Helper::fillDualInvolutions(), atlas::weyl::WeylGroup::hasTwistedCommutation(), atlas::weyl::WeylGroup::involution_expr(), atlas::cartanset::CartanClassSet::involutionMatrix(), atlas::cartanset::isImaginary(), atlas::InvolutionCompare::operator()(), atlas::kgb::InvolutionCompare::operator()(), and atlas::weyl::WeylGroup::twistedConjugate().

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Friends And Related Function Documentation

friend class WeylGroup [friend]

Definition at line 81 of file weyl.h.

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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. Definition at line 95 of file weyl.h. Referenced by operator!=(), operator<(), operator=(), operator==(), and WeylElt().

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

• /home/r0/dav/atlas.dir/atlas3/sources/structure/weyl.h
• /home/r0/dav/atlas.dir/atlas3/sources/structure/weyl.cpp

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