atlas::prerootdata Namespace Reference

Classes
class	atlas::prerootdata::PreRootDatum
	Root datum specified by user interaction. More...
Functions
void	cartanMatrix (latticetypes::LatticeMatrix &cm, const lietype::LieType &lt)
	Puts in cm the Cartan matrix corresponding to the Lie type lt.
void	cartanMatrix (latticetypes::LatticeMatrix &cm, const lietype::SimpleLieType &slt)
	Puts in cm the Cartan matrix corresponding to the simple Lie type slt.

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Function Documentation

void atlas::prerootdata::cartanMatrix (  latticetypes::LatticeMatrix &  cm, const lietype::SimpleLieType &  slt )

Puts in cm the Cartan matrix corresponding to the simple Lie type slt. Algorithm: case by case. The matrix is initialized to zero (of the correct size), then the non-zero entries are added. Definition at line 169 of file prerootdata.cpp. References atlas::latticetypes::LatticeMatrix, atlas::lietype::rank(), atlas::matrix::Matrix< C >::resize(), and atlas::lietype::type().

void atlas::prerootdata::cartanMatrix (  latticetypes::LatticeMatrix &  cm, const lietype::LieType &  lt )

Puts in cm the Cartan matrix corresponding to the Lie type lt. Algorithm: the matrix is block diagonal, one block for each simple Lie type in lt. The matrix is square, of size equal to the rank. Torus factors contribute blocks of zeros. The cartanMatrix function defined in the namespace rootdata, and printed by the cmatrix command, is of size equal to the semisimple rank. The columns of cm^t express the simple roots in the basis of fundamental weights. The columns of cm express the simple coroots in the basis of fundamental coweights. Definition at line 132 of file prerootdata.cpp. References atlas::matrix::Matrix< C >::copy(), atlas::latticetypes::LatticeMatrix, atlas::lietype::rank(), and atlas::matrix::Matrix< C >::resize(). Referenced by atlas::prerootdata::PreRootDatum::PreRootDatum(), and atlas::tits::TitsGroup::TitsGroup().

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