/home/r0/dav/atlas.dir/atlas3/sources/structure/weyl_fwd.h File Reference

Class declarations and type definitions for WeylGroup. More...

#include <vector>
#include "constants.h"

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Namespaces
namespace	atlas
namespace	atlas::weyl
Typedefs
typedef WeylElt	TwistedInvolution
typedef std::vector< WeylElt >	WeylEltList
typedef std::vector< TwistedInvolution >	TwistedInvolutionList
typedef unsigned char	Generator
	Represents a simple root reflection (one of the standard generators of W).
typedef unsigned char	EltPiece
	Represents a minimal length coset representative for one of the parabolic subquotients W_{i-1}\W_i.
typedef std::vector< Generator >	WeylWord

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Detailed Description

Class declarations and type definitions for WeylGroup.

Definition in file weyl_fwd.h.

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Typedef Documentation

typedef unsigned char atlas::weyl::EltPiece

Represents a minimal length coset representative for one of the parabolic subquotients W_{i-1}\W_i. Definition at line 44 of file weyl_fwd.h. Referenced by atlas::dihedralMin(), atlas::dihedralShift(), atlas::weyl::WeylGroup::multIn(), atlas::weyl::WeylElt::operator[](), atlas::weyl::Transducer::shift(), and atlas::weyl::Transducer::Transducer().

typedef unsigned char atlas::weyl::Generator

Represents a simple root reflection (one of the standard generators of W). Definition at line 38 of file weyl_fwd.h. Referenced by atlas::cartanset::cayleyPart(), atlas::weyl::WeylGroup::conjugacyClass(), atlas::cartanset::crossPart(), atlas::dihedralMin(), atlas::dihedralShift(), atlas::involutions::helper::Helper::fillCartan(), atlas::weyl::WeylGroup::involution_expr(), atlas::weyl::WeylGroup::leftDescent(), atlas::weyl::WeylGroup::min_neighbor(), atlas::weyl::WeylGroup::multIn(), atlas::weyl::RowBase::operator[](), atlas::weyl::WeylInterface::operator[](), atlas::weyl::Transducer::out(), atlas::weyl::Transducer::Transducer(), atlas::weyl::WeylGroup::twisted(), atlas::weyl::WeylGroup::twistedConjugacyClass(), atlas::weyl::WeylGroup::twistGenerator(), and atlas::weyl::WeylGroup::WeylGroup().

typedef WeylElt atlas::weyl::TwistedInvolution

Definition at line 28 of file weyl_fwd.h. Referenced by atlas::cartanset::CartanClassSet::addCartan(), atlas::kgb::KGBHelp::backtrack_seed(), atlas::cartanset::CartanClassSet::canonicalize(), atlas::kgb::FiberData::cartanClass(), atlas::cartanset::CartanClassSet::cayley(), atlas::cartanset::cayley_and_cross_part(), atlas::cartanset::cayleyPart(), atlas::kltest::checkBasePoint(), atlas::cartanset::checkDecomposition(), atlas::cartanset::CartanClassSet::classNumber(), atlas::cartanset::CartanClassSet::correlateDualForms(), atlas::cartanset::CartanClassSet::correlateForms(), atlas::cartanset::crossPart(), atlas::involutions::InvolutionSet::dualInvolution(), atlas::blocks::Block::dualInvolution(), atlas::cartanset::CartanClassSet::extend(), atlas::kgb::FiberData::FiberData(), atlas::involutions::helper::Helper::fillCartan(), atlas::involutions::helper::Helper::fillDualInvolutions(), atlas::involutions::helper::Helper::fillInvolutions(), atlas::blocks::Block::generate(), atlas::weyl::WeylGroup::hasTwistedCommutation(), atlas::weyl::WeylGroup::inverseTwistedConjugate(), atlas::kgb::KGB::involution(), atlas::involutions::InvolutionSet::involution(), atlas::blocks::Block::involution(), atlas::weyl::WeylGroup::involution_expr(), atlas::complexredgp::ComplexReductiveGroup::involutionMatrix(), atlas::cartanset::CartanClassSet::involutionMatrix(), atlas::involutions::InvolutionSet::involutionNbr(), atlas::cartanset::isImaginary(), atlas::kgb::KGBHelp::naive_seed(), atlas::InvolutionCompare::operator()(), atlas::kgb::InvolutionCompare::operator()(), atlas::cartanset::CartanClassSet::posImaginaryRootSum(), atlas::cartanset::CartanClassSet::posRealRootSum(), atlas::prettyprint::printInvolution(), atlas::cartanset::CartanClassSet::reflection(), atlas::kgb::KGB::tauPacket(), atlas::weyl::TI_Entry::TI_Entry(), atlas::tits::TitsElt::tw(), atlas::cartanset::CartanClassSet::twistedAct(), atlas::weyl::WeylGroup::twistedConjugacyClass(), atlas::weyl::WeylGroup::twistedConjugate(), atlas::weyl::WeylGroup::twistedConjugated(), atlas::cartanset::CartanClassSet::twistedInvolution(), and atlas::cartanset::CartanClassSet::updateTwistedInvolutions().

typedef std::vector<TwistedInvolution> atlas::weyl::TwistedInvolutionList

Definition at line 32 of file weyl_fwd.h. Referenced by atlas::kltest::checkBasePoint(), and atlas::weyl::WeylGroup::twistedConjugacyClass().

typedef std::vector<WeylElt> atlas::weyl::WeylEltList

Definition at line 31 of file weyl_fwd.h. Referenced by atlas::weyl::WeylGroup::reflections().

typedef std::vector<Generator> atlas::weyl::WeylWord

Definition at line 46 of file weyl_fwd.h. Referenced by atlas::weyl::WeylGroup::act(), atlas::kltest::checkBasePoint(), atlas::cartanset::CartanClassSet::correlateDualForms(), atlas::cartanset::CartanClassSet::correlateForms(), atlas::weyl::WeylGroup::hasDescent(), atlas::weyl::WeylGroup::inverse(), atlas::involutions::InvolutionSet::involutionNbr(), atlas::rootdata::longest(), atlas::prettyprint::printWeylElt(), atlas::prettyprint::printWeylList(), atlas::weyl::Transducer::Transducer(), atlas::weyl::WeylGroup::translation(), atlas::weyl::WeylGroup::twistedConjugate(), atlas::weyl::WeylGroup::word(), atlas::weyl::WeylGroup::wordPiece(), and atlas::weyl::Transducer::wordPiece().

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