atlas::latticetypes Namespace Reference

Classes
class	atlas::latticetypes::RatLatticeElt
	Element of lattice tensored with rational numbers. More...
Typedefs
typedef int	LatticeCoeff
	A LatticeElt is a vector of LatticeCoeff's; that is, an element of Z^n.
typedef std::vector< LatticeCoeff >	LatticeElt
	A LatticeElt is a vector of LatticeCoeff's; that is, an element of Z^n.
typedef std::vector< LatticeCoeff >	CoeffList
	This type of list of integers is used as the list of invariant factors in a Smith normal form.
typedef LatticeElt	Weight
typedef RatLatticeElt	RatWeight
typedef std::vector< Weight >	WeightList
typedef std::vector< RatWeight >	RatWeightList
typedef matrix::Matrix< LatticeCoeff >	LatticeMatrix
typedef bitvector::BitVector< constants::RANK_MAX >	Component
	Element of (Z/2Z)^RANK_MAX.
typedef bitvector::BitVector< constants::RANK_MAX >	SmallBitVector
typedef bitvector::BitVectorList< constants::RANK_MAX >	SmallBitVectorList
typedef bitvector::BitVector< constants::RANK_MAX+1 >	BinaryEquation
typedef bitvector::BitVectorList< constants::RANK_MAX+1 >	BinaryEquationList
typedef bitvector::BitVector< 2 *constants::RANK_MAX >	LongComponent
	Element of (Z/2Z)^2*RANK_MAX.
typedef bitvector::BitMatrix< constants::RANK_MAX >	BinaryMap
	Square matrix of size RANK_MAX with entries in Z/2Z.
typedef subquotient::Subspace< constants::RANK_MAX >	SmallSubspace
	Subgroup of (Z/2Z)^RANK_MAX.
typedef subquotient::Subquotient< constants::RANK_MAX >	SmallSubquotient
	Subquotient of (Z/2Z)^RANK_MAX.
typedef std::vector< Component >	ComponentList
	List of elements of (Z/2Z)^RANK_MAX.
typedef std::vector< LongComponent >	LongComponentList
	List of elements of (Z/2Z)^2*RANK_MAX.
Functions
LatticeElt &	operator+= (LatticeElt &v, const LatticeElt &w)
LatticeElt &	operator-= (LatticeElt &v, const LatticeElt &w)
LatticeElt &	operator *= (LatticeElt &v, const LatticeCoeff &c)
LatticeElt &	operator/= (LatticeElt &v, const LatticeCoeff &d)
LatticeElt &	operator- (LatticeElt &v)
bool	isZero (const LatticeElt &v)
LatticeCoeff	scalarProduct (const LatticeElt &v, const LatticeElt &w)
LatticeCoeff	scalarProduct (const RatLatticeElt &v, const LatticeElt &w)
Variables
const LatticeCoeff	ZeroCoeff = 0
const LatticeCoeff	OneCoeff = 1

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Typedef Documentation

typedef bitvector::BitVector<constants::RANK_MAX+1> atlas::latticetypes::BinaryEquation

Definition at line 93 of file latticetypes_fwd.h. Referenced by atlas::compactEquations(), atlas::gradings::findGrading(), atlas::kgb::KGBHelp::grading_seed(), and atlas::noncompactEquations().

typedef bitvector::BitVectorList<constants::RANK_MAX+1> atlas::latticetypes::BinaryEquationList

Definition at line 95 of file latticetypes_fwd.h. Referenced by atlas::compactEquations(), atlas::gradings::findGrading(), atlas::kgb::KGBHelp::grading_seed(), and atlas::noncompactEquations().

typedef bitvector::BitMatrix<constants::RANK_MAX> atlas::latticetypes::BinaryMap

Square matrix of size RANK_MAX with entries in Z/2Z. Used to represent for instance the map on (dual) component groups of real tori induced by a lattice map. Definition at line 108 of file latticetypes_fwd.h. Referenced by atlas::topology::Connectivity::Connectivity(), atlas::tori::dualPi0(), atlas::kgb::FiberData::FiberData(), atlas::cartanclass::Fiber::gradingGroup(), atlas::cartanclass::Fiber::makeFiberMap(), and atlas::makeTopology().

typedef std::vector<LatticeCoeff> atlas::latticetypes::CoeffList

This type of list of integers is used as the list of invariant factors in a Smith normal form. Definition at line 61 of file latticetypes_fwd.h.

typedef bitvector::BitVector<constants::RANK_MAX> atlas::latticetypes::Component

Element of (Z/2Z)^RANK_MAX. Used to represent an element of a component group of a real torus; this is why it turns up in connection with lattices. Definition at line 78 of file latticetypes_fwd.h.

typedef std::vector<Component> atlas::latticetypes::ComponentList

List of elements of (Z/2Z)^RANK_MAX. Used to represent a subset of the group of connected components of a real torus. Definition at line 131 of file latticetypes_fwd.h.

typedef int atlas::latticetypes::LatticeCoeff

A LatticeElt is a vector of LatticeCoeff's; that is, an element of Z^n. Definition at line 43 of file latticetypes_fwd.h. Referenced by atlas::interactive_lattice::adjustBasis(), atlas::lattice::baseChange(), atlas::checkGenerator(), atlas::checkInvolution(), atlas::latticetypes::RatLatticeElt::denominator(), atlas::interactive_lattice::getGenerators(), atlas::makeRootBasis(), atlas::readGenerator(), atlas::rootdata::reflectionMatrix(), atlas::rootdata::RootDatum::RootDatum(), scalarProduct(), and atlas::weyl::Transducer::Transducer().

typedef std::vector<LatticeCoeff> atlas::latticetypes::LatticeElt

A LatticeElt is a vector of LatticeCoeff's; that is, an element of Z^n. Definition at line 54 of file latticetypes_fwd.h. Referenced by atlas::latticetypes::RatLatticeElt::numerator(), operator *=(), operator+=(), operator-(), operator-=(), operator/=(), atlas::lattice::perp(), and scalarProduct().

typedef matrix::Matrix<LatticeCoeff> atlas::latticetypes::LatticeMatrix

Definition at line 70 of file latticetypes_fwd.h. Referenced by atlas::cartanset::CartanClassSet::addCartan(), atlas::lietype::addCompactInvolution(), atlas::lietype::addDInvolution(), atlas::lietype::addMinusIdentity(), atlas::lietype::addSimpleInvolution(), atlas::cartanclass::Fiber::adjointInvolution(), atlas::interpreter::ann_mod_wrapper(), atlas::interpreter::annihilator_modulo(), atlas::lattice::baseChange(), atlas::interpreter::based_involution_wrapper(), atlas::interpreter::basic_involution_wrapper(), atlas::abelian::basis(), atlas::bitvector::BitMatrix< constants::RANK_MAX >::BitMatrix(), atlas::interpreter::block_sizes_wrapper(), atlas::interpreter::Cartan_matrix_wrapper(), atlas::interpreter::Cartan_order_matrix_wrapper(), atlas::cartanclass::CartanClass::CartanClass(), atlas::cartanset::CartanClassSet::CartanClassSet(), atlas::rootdata::cartanMatrix(), atlas::rootdata::RootDatum::cartanMatrix(), atlas::prerootdata::cartanMatrix(), atlas::interpreter::cast_intlistlist_to_latmat(), atlas::interpreter::check_involution(), atlas::cartanset::checkDecomposition(), atlas::checkInvolution(), atlas::interpreter::classify_involution(), atlas::cmatrix_f(), atlas::complexredgp::ComplexReductiveGroup::ComplexReductiveGroup(), atlas::topology::Connectivity::Connectivity(), atlas::interpreter::coroot_radical_wrapper(), atlas::interpreter::coroots_wrapper(), atlas::cartanset::CartanClassSet::correlateDualForms(), atlas::testrun::CoveringIterator::CoveringIterator(), atlas::interpreter::datum_Cartan_wrapper(), atlas::interpreter::diagonal_wrapper(), atlas::realredgp::RealReductiveGroup::distinguished(), atlas::complexredgp::ComplexReductiveGroup::distinguished(), atlas::cartanset::CartanClassSet::distinguished(), atlas::interpreter::dual_occurrence_matrix_wrapper(), atlas::rootdata::dualBasedInvolution(), atlas::cartanset::CartanClassSet::dualDistinguished(), atlas::cartanclass::dualFiber(), atlas::tori::dualPi0(), atlas::dynkin::DynkinDiagram::DynkinDiagram(), atlas::interpreter::matrix2_conversion::evaluate(), atlas::interpreter::matrix_conversion::evaluate(), atlas::cartanclass::Fiber::Fiber(), atlas::kgb::FiberData::FiberData(), atlas::fillCoxMatrix(), atlas::rootdata::RootDatum::fillStatus(), atlas::fullMinusBasis(), atlas::fullPlusBasis(), atlas::interactive::getInnerClass(), atlas::interactive::getInteractive(), atlas::interactive_lattice::getLattice(), atlas::interpreter::GL_wrapper(), atlas::interpreter::id_mat_wrapper(), atlas::lattice::inverseBaseChange(), atlas::tori::RealTorus::involution(), atlas::lietype::involution(), atlas::cartanclass::CartanClass::involution(), atlas::cartanclass::Fiber::involution(), atlas::cartanclass::InvolutionData::InvolutionData(), atlas::cartanset::CartanClassSet::involutionMatrix(), atlas::cartanset::isImaginary(), atlas::rootdata::lieType(), atlas::dynkin::lieType(), atlas::complexredgp::lieType(), atlas::rootdata::longest(), atlas::testrun::CoveringIterator::makeBasis(), atlas::makeCorootBasis(), atlas::makeOrthogonal(), atlas::makeRootBasis(), atlas::cartanclass::CartanClass::makeSimpleComplex(), atlas::tits::makeTwist(), atlas::interpreter::matrix_value::matrix_value(), atlas::tori::minusBasis(), atlas::tori::minusMatrix(), atlas::lattice::mod2(), atlas::lattice::numeratorMatrix(), atlas::interpreter::occurrence_matrix_wrapper(), atlas::lattice::perp(), atlas::tori::plsuBasis(), atlas::tori::plusBasis(), atlas::tori::plusMatrix(), atlas::prerootdata::PreRootDatum::PreRootDatum(), atlas::testprint::print(), atlas::interpreter::print_gradings_wrapper(), atlas::testprint::printCartanMatrix(), atlas::cartan_io::printGradings(), atlas::realredgp::RealReductiveGroup::RealReductiveGroup(), atlas::rootdata::reflectionMatrix(), atlas::interpreter::root_coradical_wrapper(), atlas::interpreter::root_datum_wrapper(), atlas::rootdata::RootDatum::RootDatum(), atlas::rootdata::RootDatum::rootPermutation(), atlas::rootdata::RootDatum::rootReflection(), atlas::interpreter::roots_wrapper(), atlas::interpreter::simple_coroots_wrapper(), atlas::interpreter::simple_roots_wrapper(), atlas::interpreter::SL_wrapper(), atlas::interpreter::Smith_basis_wrapper(), atlas::interpreter::Smith_Cartan_wrapper(), atlas::interpreter::Smith_wrapper(), atlas::interactive_lattice::smithBasis(), atlas::interpreter::smithBasis(), atlas::tits::TitsGroup::TitsGroup(), atlas::rootdata::toDistinguished(), atlas::abelian::toEndomorphism(), atlas::rootdata::toMatrix(), atlas::weyl::Transducer::Transducer(), atlas::interpreter::type_of_datum(), atlas::involutions::helper::Helper::weylCorrelation(), atlas::weyl::WeylGroup::WeylGroup(), and atlas::rootdata::RootDatum::word_of_inverse_matrix().

typedef bitvector::BitVector<2*constants::RANK_MAX> atlas::latticetypes::LongComponent

Element of (Z/2Z)^2*RANK_MAX. Definition at line 100 of file latticetypes_fwd.h.

typedef std::vector<LongComponent> atlas::latticetypes::LongComponentList

List of elements of (Z/2Z)^2*RANK_MAX. Definition at line 136 of file latticetypes_fwd.h.

typedef RatLatticeElt atlas::latticetypes::RatWeight

Definition at line 65 of file latticetypes_fwd.h. Referenced by atlas::interactive_lattice::getGenerators(), atlas::readGenerator(), and atlas::rootdata::RootDatum::RootDatum().

typedef std::vector<RatWeight> atlas::latticetypes::RatWeightList

Definition at line 68 of file latticetypes_fwd.h. Referenced by atlas::interactive_lattice::getLattice(), and atlas::makeOrthogonal().

typedef bitvector::BitVector<constants::RANK_MAX> atlas::latticetypes::SmallBitVector

Definition at line 84 of file latticetypes_fwd.h. Referenced by atlas::cartanclass::Fiber::adjointMAlphas(), atlas::kgb::KGBHelp::backtrack_seed(), atlas::cartanclass::Fiber::gradingGroup(), atlas::cartanclass::Fiber::gradingRep(), atlas::realweyl::RealWeyl::imaginaryR(), atlas::kgb::KGBHelp::is_compact(), atlas::cartanclass::Fiber::makeFiberMap(), atlas::cartanclass::Fiber::makeRealFormPartition(), atlas::cartanset::makeRepresentative(), atlas::cartanclass::Fiber::makeStrongRepresentatives(), atlas::cartanclass::Fiber::mAlpha(), atlas::kgb::KGBHelp::naive_seed(), atlas::realweyl::RealWeyl::realR(), atlas::realweyl::RealWeylGenerators::RealWeylGenerators(), atlas::rGenerators(), atlas::subquotient::subquotientMap(), atlas::tits::TitsGroup::TitsGroup(), and atlas::cartanclass::Fiber::toAdjoint().

typedef bitvector::BitVectorList<constants::RANK_MAX> atlas::latticetypes::SmallBitVectorList

Definition at line 86 of file latticetypes_fwd.h. Referenced by atlas::topology::Connectivity::dualComponentReps(), atlas::realredgp::RealReductiveGroup::dualComponentReps(), atlas::tori::dualPi0(), atlas::kgb::FiberData::FiberData(), atlas::cartanclass::Fiber::gradingGroup(), atlas::cartanclass::Fiber::gradingRep(), atlas::realweyl::RealWeyl::imaginaryR(), atlas::cartanclass::Fiber::makeFiberMap(), atlas::cartanclass::Fiber::makeGradingShifts(), atlas::cartanclass::Fiber::makeRealFormPartition(), atlas::cartanset::makeRepresentative(), atlas::cartanclass::Fiber::makeStrongRepresentatives(), atlas::makeTopology(), atlas::testprint::printComponents(), atlas::realweyl::RealWeyl::realR(), and atlas::rGenerators().

typedef subquotient::Subquotient<constants::RANK_MAX> atlas::latticetypes::SmallSubquotient

Subquotient of (Z/2Z)^RANK_MAX. Definition at line 123 of file latticetypes_fwd.h. Referenced by atlas::cartanclass::Fiber::adjointFiberGroup(), atlas::tori::dualPi0(), atlas::cartanclass::Fiber::fiberGroup(), atlas::cartanclass::Fiber::makeAdjointFiberGroup(), atlas::cartanclass::Fiber::makeFiberGroup(), atlas::cartanclass::Fiber::makeRealFormPartition(), atlas::makeTopology(), and atlas::tori::RealTorus::topology().

typedef subquotient::Subspace<constants::RANK_MAX> atlas::latticetypes::SmallSubspace

Subgroup of (Z/2Z)^RANK_MAX. Used to represent a subgroup of the group of connected components of a real torus. Definition at line 116 of file latticetypes_fwd.h. Referenced by atlas::kgb::FiberData::FiberData(), atlas::cartanclass::Fiber::gradingGroup(), and atlas::kgb::FiberData::mod_space().

typedef LatticeElt atlas::latticetypes::Weight

Definition at line 64 of file latticetypes_fwd.h. Referenced by atlas::interactive_lattice::adjustBasis(), atlas::lattice::baseChange(), atlas::abelian::basis(), atlas::interpreter::cast_intlistlist_to_latmat(), atlas::topology::Connectivity::Connectivity(), atlas::interpreter::matrix2_conversion::evaluate(), atlas::interpreter::matrix_conversion::evaluate(), atlas::interactive_lattice::getGenerators(), atlas::interactive_lattice::getLattice(), atlas::gradings::gradingType(), atlas::lattice::inverseBaseChange(), atlas::rootdata::longest(), atlas::testrun::CoveringIterator::makeBasis(), atlas::makeCorootBasis(), atlas::makeRootBasis(), atlas::tori::minusMatrix(), atlas::orthogonalMAlpha(), atlas::tori::plusMatrix(), atlas::rootdata::reflectionMatrix(), atlas::rootdata::RootDatum::reflectionWord(), atlas::rootdata::RootDatum::RootDatum(), atlas::rootdata::strongOrthogonalize(), atlas::rootdata::sumIsRoot(), atlas::rootdata::toDistinguished(), atlas::rootdata::toPositive(), atlas::rootdata::toWeylWord(), atlas::rootdata::RootDatum::twoRho(), and atlas::rootdata::RootDatum::word_of_inverse_matrix().

typedef std::vector<Weight> atlas::latticetypes::WeightList

Definition at line 67 of file latticetypes_fwd.h. Referenced by atlas::abelian::basis(), atlas::interpreter::check_involution(), atlas::checkInvolution(), atlas::compactEquations(), atlas::topology::Connectivity::Connectivity(), atlas::testrun::CoveringIterator::CoveringIterator(), atlas::tori::dualPi0(), atlas::fillPositiveRoots(), atlas::fillRoots(), atlas::rootdata::RootDatum::fillStatus(), atlas::gradings::findGrading(), atlas::fullMinusBasis(), atlas::fullPlusBasis(), atlas::interactive::getInteractive(), atlas::interactive_lattice::getLattice(), atlas::gradings::gradingType(), atlas::testrun::CoveringIterator::makeBasis(), atlas::makeOrthogonal(), atlas::tori::minusBasis(), atlas::tori::minusMatrix(), atlas::testrun::CoveringIterator::operator++(), atlas::lattice::perp(), atlas::tori::plusBasis(), atlas::tori::plusMatrix(), and atlas::testprint::print().

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Function Documentation

bool atlas::latticetypes::isZero (  const LatticeElt &  v  )

Definition at line 119 of file latticetypes.cpp. Referenced by atlas::makeRootBasis().

LatticeElt & atlas::latticetypes::operator *= (  LatticeElt &  v, const LatticeCoeff &  c )

Definition at line 63 of file latticetypes.cpp. References LatticeElt.

LatticeElt & atlas::latticetypes::operator+= (  LatticeElt &  v, const LatticeElt &  w )

Definition at line 37 of file latticetypes.cpp. References LatticeElt. Referenced by atlas::interpreter::smithBasis().

LatticeElt & atlas::latticetypes::operator- (  LatticeElt &  v  )

Definition at line 91 of file latticetypes.cpp. References LatticeElt.

LatticeElt & atlas::latticetypes::operator-= (  LatticeElt &  v, const LatticeElt &  w )

Definition at line 50 of file latticetypes.cpp. References LatticeElt.

LatticeElt & atlas::latticetypes::operator/= (  LatticeElt &  v, const LatticeCoeff &  d )

Definition at line 76 of file latticetypes.cpp. References LatticeElt.

LatticeCoeff atlas::latticetypes::scalarProduct (  const RatLatticeElt &  v, const LatticeElt &  w )

Definition at line 150 of file latticetypes.cpp. References atlas::latticetypes::RatLatticeElt::denominator(), LatticeCoeff, LatticeElt, and atlas::latticetypes::RatLatticeElt::numerator(). Referenced by atlas::cartanset::CartanClassSet::canonicalize(), atlas::rootdata::RootDatum::cartan(), atlas::rootdata::cartanMatrix(), atlas::rootdata::RootDatum::cartanMatrix(), atlas::cartanclass::Fiber::gradingGroup(), atlas::rootdata::RootDatum::inSimpleRoots(), atlas::kgb::KGBHelp::is_compact(), atlas::rootdata::RootDatum::isOrthogonal(), atlas::cartanclass::Fiber::makeGradingShifts(), atlas::testprint::printCartanMatrix(), atlas::tits::TitsGroup::reflect(), atlas::bitset::BitSet< numFlags >::scalarProduct(), atlas::rootdata::RootDatum::scalarProduct(), atlas::kgb::KGBHelp::simple_grading(), atlas::rootdata::toPositive(), and atlas::rootdata::RootDatum::toSimpleWeights().

LatticeCoeff atlas::latticetypes::scalarProduct (  const LatticeElt &  v, const LatticeElt &  w )

Definition at line 133 of file latticetypes.cpp. References LatticeCoeff.

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Variable Documentation

const LatticeCoeff atlas::latticetypes::OneCoeff = 1

Definition at line 46 of file latticetypes_fwd.h.

const LatticeCoeff atlas::latticetypes::ZeroCoeff = 0

Definition at line 45 of file latticetypes_fwd.h.

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