atlas::dynkin Namespace Reference

Classes
class	atlas::dynkin::DynkinDiagram
	A Dynkin diagram of at most RANK_MAX vertices. More...
Typedefs
typedef std::pair< size_t, size_t >	Edge
typedef unsigned	Multiplicity
Functions
void	bourbaki (setutils::Permutation &a, const DynkinDiagram &d)
void	components (bitset::RankFlagsList &cl, const DynkinDiagram &d)
void	lieType (lietype::LieType &lt, const latticetypes::LatticeMatrix &cm)
lietype::LieType	lieType (const latticetypes::LatticeMatrix &cm)
void	normalize (setutils::Permutation &a, const DynkinDiagram &d)
void	components (bitset::RankFlagsList &, const DynkinDiagram &, const bitset::RankFlags &)

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Typedef Documentation

typedef std::pair<size_t, size_t> atlas::dynkin::Edge

Since a Dynkin diagram will be a bitset (a subset of RANK_MAX elements, the possible vertices 0, 1,...,RANK_MAX-1), an Edge is a pair of numbers (between 0 and RANK_MAX-1). Definition at line 35 of file dynkin.h. Referenced by atlas::dynkin::DynkinDiagram::cartanEntry(), atlas::dynkin::DynkinDiagram::DynkinDiagram(), atlas::irreducibleType(), atlas::dynkin::DynkinDiagram::labelEdge(), atlas::typeBNormalize(), atlas::typeCNormalize(), atlas::typeFNormalize(), and atlas::typeGNormalize().

typedef unsigned atlas::dynkin::Multiplicity

The Multiplicity of an Edge should be 1, 2, or 3. Definition at line 40 of file dynkin.h. Referenced by atlas::dynkin::DynkinDiagram::edgeMultiplicity(), and atlas::dynkin::DynkinDiagram::maxMultiplicity().

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Function Documentation

void atlas::dynkin::bourbaki (  setutils::Permutation &  a, const DynkinDiagram &  d )

Synopsis: writes in |a| some permutation that will take d to Bourbaki form This means that nodes of the diagram |d| taken in the order |a[0],...,a[r-1]| traverse each of its connected components consecutively, and in the order prescribed by the the Bourbaki conventions for the type of that component Definition at line 246 of file dynkin.cpp. References atlas::componentNormalize(), atlas::componentOrder(), components(), atlas::irreducibleType(), atlas::dynkin::DynkinDiagram::rank(), and atlas::lietype::TypeLetter. Referenced by atlas::interpreter::print_gradings_wrapper(), and atlas::cartan_io::printGradings().

void components (  bitset::RankFlagsList &  , const DynkinDiagram &  , const bitset::RankFlags &  )

Referenced by atlas::interpreter::check_involution().

void atlas::dynkin::components (  bitset::RankFlagsList &  cl, const DynkinDiagram &  d )

Writes in cl the list of the connected components of d. Definition at line 290 of file dynkin.cpp. References atlas::dynkin::DynkinDiagram::component(), atlas::dynkin::DynkinDiagram::rank(), RankFlags, and atlas::bitset::set(). Referenced by bourbaki(), lieType(), and normalize().

lietype::LieType atlas::dynkin::lieType (  const latticetypes::LatticeMatrix &  cm  )

Definition at line 338 of file dynkin.cpp. References atlas::latticetypes::LatticeMatrix, and lieType().

void atlas::dynkin::lieType (  lietype::LieType &  lt, const latticetypes::LatticeMatrix &  cm )

Synopsis: writes in lt the Lie type of the Cartan matrix cm. Definition at line 318 of file dynkin.cpp. References components(), atlas::irreducibleType(), atlas::latticetypes::LatticeMatrix, atlas::dynkin::DynkinDiagram::rank(), atlas::lietype::SimpleLieType, and atlas::lietype::TypeLetter. Referenced by lieType().

void atlas::dynkin::normalize (  setutils::Permutation &  a, const DynkinDiagram &  d )

Synopsis: writes in a a permutation that will take d to normal form This means that components of d are numbered consecutively, and that each component is normalized according to the Bourbaki conventions for the exceptional types, opposite-to-Bourbaki for the classical ones (this is the right ordering for the convenient implementation of Weyl groups.) Definition at line 343 of file dynkin.cpp. References atlas::componentNormalize(), atlas::componentOrder(), components(), and atlas::dynkin::DynkinDiagram::rank(). Referenced by atlas::subquotient::Subspace< dim >::Subspace(), and atlas::weyl::WeylGroup::WeylGroup().

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