atlas::tori Namespace Reference

Classes
class	atlas::tori::RealTorus
	Represents a torus defined over R. More...
Functions
void	dualPi0 (LT::SmallSubquotient &dpi0, const LT::LatticeMatrix &q)
void	plusBasis (latticetypes::WeightList &pb, const latticetypes::LatticeMatrix &i)
	Puts in mb a basis for the +1 eigenspace of the involution;.
latticetypes::WeightList	plsuBasis (const latticetypes::LatticeMatrix &i)
void	minusBasis (latticetypes::WeightList &mb, const latticetypes::LatticeMatrix &i)
latticetypes::WeightList	minusBasis (const latticetypes::LatticeMatrix &i)
void	minusMatrix (latticetypes::LatticeMatrix &qm, const latticetypes::LatticeMatrix &q, const RealTorus &t)
void	plusMatrix (latticetypes::LatticeMatrix &qp, const latticetypes::LatticeMatrix &q, const RealTorus &t)
void	minusBasis (LT::WeightList &, const LT::LatticeMatrix &)
LT::WeightList	minusBasis (const LT::LatticeMatrix &)
void	minusMatrix (LT::LatticeMatrix &, const LT::LatticeMatrix &, const RealTorus &)
void	plusBasis (LT::WeightList &, const LT::LatticeMatrix &)
LT::WeightList	plusBasis (const LT::LatticeMatrix &)
void	plusMatrix (LT::LatticeMatrix &, const LT::LatticeMatrix &, const RealTorus &)

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Function Documentation

void atlas::tori::dualPi0 (  LT::SmallSubquotient &  dpi0, const LT::LatticeMatrix &  q )

Synopsis: puts in dpi0 what would have been the topology field for the corresponding torus. Precondition: q is an involution matrix; its size doesn't exceed RankMax; Explanation: this is canonically the dual of the component group; see makeTopology. Definition at line 201 of file tori.cpp. References atlas::latticetypes::BinaryMap, atlas::matrix::identityMatrix(), atlas::bitvector::BitMatrix< dim >::kernel(), atlas::latticetypes::LatticeMatrix, atlas::matrix::Matrix< C >::numColumns(), atlas::matrix::Matrix< C >::numRows(), plusBasis(), atlas::subquotient::Subquotient< dim >::rank(), atlas::latticetypes::SmallBitVectorList, atlas::latticetypes::SmallSubquotient, atlas::subquotient::Subquotient< dim >::swap(), and atlas::latticetypes::WeightList. Referenced by atlas::cartanclass::Fiber::makeAdjointFiberGroup(), and atlas::cartanclass::Fiber::makeFiberGroup().

LT::WeightList minusBasis (  const LT::LatticeMatrix &   )

void minusBasis (  LT::WeightList &  , const LT::LatticeMatrix &  )

latticetypes::WeightList minusBasis (  const latticetypes::LatticeMatrix &  i  )

Definition at line 331 of file tori.cpp. References atlas::latticetypes::LatticeMatrix, and minusBasis().

void minusBasis (  latticetypes::WeightList &  mb, const latticetypes::LatticeMatrix &  i )

Synopsis: puts in mb a basis for the -1 eigenspace of the involution. Algorithm: the vectors e-i(e), when e runs through b, generate a lattice commensurate with the eigenspace. Thus a smith basis for this lattice will do the trick. Definition at line 289 of file tori.cpp. References atlas::matrix::initBasis(), atlas::latticetypes::LatticeMatrix, atlas::matrix::Matrix< C >::numColumns(), atlas::smithnormal::smithNormal(), and atlas::latticetypes::WeightList. Referenced by minusBasis().

void minusMatrix (  LT::LatticeMatrix &  , const LT::LatticeMatrix &  , const RealTorus &  )

void minusMatrix (  latticetypes::LatticeMatrix &  qm, const latticetypes::LatticeMatrix &  q, const RealTorus &  t )

Synopsis: writes in qm the matrix of the restriction of q to X_-. Precondition: q commutes with the involution; Definition at line 336 of file tori.cpp. References atlas::matrix::Matrix< C >::apply(), atlas::latticetypes::LatticeMatrix, atlas::tori::RealTorus::minusLattice(), atlas::tori::RealTorus::rank(), atlas::matrix::Matrix< C >::resize(), atlas::tori::RealTorus::toMinus(), atlas::latticetypes::Weight, and atlas::latticetypes::WeightList.

latticetypes::WeightList plsuBasis (  const latticetypes::LatticeMatrix &  i  )

Definition at line 284 of file tori.cpp. References atlas::latticetypes::LatticeMatrix, and plusBasis().

LT::WeightList plusBasis (  const LT::LatticeMatrix &   )

void plusBasis (  LT::WeightList &  , const LT::LatticeMatrix &  )

void plusBasis (  latticetypes::WeightList &  pb, const latticetypes::LatticeMatrix &  i )

Puts in mb a basis for the +1 eigenspace of the involution;. Synopsis: puts in mb a basis for the +1 eigenspace of the involution; Algorithm: the vectors e+i(e), when e runs through b, generate a lattice commensurate with the eigenspace. Definition at line 245 of file tori.cpp. References atlas::matrix::initBasis(), atlas::latticetypes::LatticeMatrix, atlas::matrix::Matrix< C >::numColumns(), atlas::smithnormal::smithNormal(), and atlas::latticetypes::WeightList. Referenced by dualPi0(), and plsuBasis().

void plusMatrix (  LT::LatticeMatrix &  , const LT::LatticeMatrix &  , const RealTorus &  )

void plusMatrix (  latticetypes::LatticeMatrix &  qp, const latticetypes::LatticeMatrix &  q, const RealTorus &  t )

Synopsis: writes in qp the matrix of the restriction of q to X_+. Precondition: q commutes with the involution; Definition at line 361 of file tori.cpp. References atlas::matrix::Matrix< C >::apply(), atlas::latticetypes::LatticeMatrix, atlas::tori::RealTorus::plusLattice(), atlas::tori::RealTorus::rank(), atlas::matrix::Matrix< C >::resize(), atlas::tori::RealTorus::toPlus(), atlas::latticetypes::Weight, and atlas::latticetypes::WeightList.

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