atlas::kl Namespace Reference

Classes
class	atlas::kl::KLPolEntry
class	atlas::kl::KLContext
	Calculates and stores the Kazhdan-Lusztig polynomials for a block of representations of G. More...
Typedefs
typedef std::vector< KLPol >	KLStore
typedef KLStore::const_reference	KLPolRef
typedef std::vector< KLIndex >	KLRow
typedef unsigned int	KLCoeff
	Coefficient of a KL polynomial.
typedef polynomials::Polynomial< KLCoeff >	KLPol
	Polynomial with coefficients of type KLCoeff.
typedef unsigned int	KLIndex
typedef KLCoeff	MuCoeff
typedef std::pair< std::vector< blocks::BlockElt >, std::vector< MuCoeff > >	MuRow
Functions
void	wGraph (wgraph::WGraph &wg, const KLContext &klc)
	Puts in wg the W-graph for this block.
const KLPol	One (0)
	Polynomial 1.q^0.
void	alert (unsigned int i)
Variables
const KLPol	Zero
	Polynomial 0, which is stored as a vector of size 0.
const KLCoeff	UndefKLCoeff = std::numeric_limits<KLCoeff>::max()
const KLCoeff	UndefMuCoeff = std::numeric_limits<MuCoeff>::max()

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Typedef Documentation

typedef unsigned int atlas::kl::KLCoeff

Coefficient of a KL polynomial. Must be a standard unsigned type; now "unsigned" which [at least on my Mac; not sure what the standard says - DV 8/14/06] is unsigned long. Definition at line 37 of file kl_fwd.h.

typedef unsigned int atlas::kl::KLIndex

Definition at line 44 of file kl_fwd.h. Referenced by atlas::kl::helper::Helper::fillMuRow(), atlas::kl::helper::Thicket::one(), and atlas::kl::helper::Thicket::zero().

typedef polynomials::Polynomial<KLCoeff> atlas::kl::KLPol

Polynomial with coefficients of type KLCoeff. Definition at line 42 of file kl_fwd.h. Referenced by atlas::kl::helper::Thicket::ascentCompute(), atlas::kltest::dualityVerify(), atlas::kl::helper::Thicket::edgeCompute(), atlas::kl::helper::Helper::fill(), atlas::kl::KLPolEntry::KLPolEntry(), atlas::kl_io::printAllKL(), atlas::kl_io::printKLList(), and atlas::kl::helper::Helper::writeRow().

typedef KLStore::const_reference atlas::kl::KLPolRef

Definition at line 48 of file kl.h. Referenced by atlas::kl::helper::Helper::fillMuRow(), atlas::kl::helper::Helper::klPol(), atlas::kl::KLContext::klPol(), atlas::kl::helper::Thicket::klPol(), atlas::kl::helper::Helper::lengthOneMu(), and atlas::kl::helper::Helper::muCorrection().

typedef std::vector<KLIndex> atlas::kl::KLRow

Definition at line 50 of file kl.h. Referenced by atlas::kl::KLContext::klPol(), atlas::kl::KLContext::klRow(), atlas::kl::helper::Thicket::klRow(), and atlas::kl::helper::Helper::writeRow().

typedef std::vector<KLPol> atlas::kl::KLStore

Definition at line 46 of file kl.h. Referenced by atlas::kl::KLContext::polStore(), and atlas::kl::helper::Thicket::store().

typedef KLCoeff atlas::kl::MuCoeff

Definition at line 47 of file kl_fwd.h. Referenced by atlas::kl::helper::Helper::fillMuRow(), atlas::kl::helper::Helper::goodDescentMu(), atlas::kl::helper::Helper::lengthOneMu(), atlas::kl::KLContext::mu(), atlas::kl::helper::Helper::muCorrection(), atlas::kl::helper::Helper::type2Mu(), and wGraph().

typedef std::pair<std::vector<blocks::BlockElt>,std::vector<MuCoeff> > atlas::kl::MuRow

Definition at line 50 of file kl_fwd.h. Referenced by atlas::kl::KLContext::mu(), atlas::kl::helper::Helper::muCorrection(), atlas::kl::KLContext::muRow(), and wGraph().

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Function Documentation

void alert (  unsigned int  i  )

const KLPol One (  0   )

Polynomial 1.q^0.

void atlas::kl::wGraph (  wgraph::WGraph &  wg, const KLContext &  klc )

Puts in wg the W-graph for this block. Explanation: the W-graph is a graph with one vertex for each element of the block; the corresponding descent set is the tau-invariant, i.e. the set of generators s that are either complex descents, real type I or II, or imaginary compact. Let x < y in the block such that mu(x,y) != 0, and descent(x) != descent(y). Then there is an edge from x to y unless descent(x) is contained in descent(y), and an edge from y to x unless descent(y) is contained in descent(x). Note that the latter containment always holds when the length difference is > 1, so that in that case there will only be an edge from x to y (the edge must be there because we already assumed that the descent sets were not equal.) In both cases, the coefficient corresponding to the edge is mu(x,y). NOTE: if I'm not mistaken, the edgelists come already out sorted. Definition at line 2072 of file kl.cpp. References atlas::wgraph::WGraph::coeffList(), atlas::wgraph::WGraph::descent(), atlas::kl::KLContext::descentSet(), atlas::wgraph::WGraph::edgeList(), atlas::kl::KLContext::length(), MuCoeff, atlas::kl::KLContext::muRow(), MuRow, RankFlags, atlas::wgraph::WGraph::reset(), atlas::wgraph::WGraph::resize(), and atlas::kl::KLContext::size().

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Variable Documentation

const KLCoeff atlas::kl::UndefKLCoeff = std::numeric_limits<KLCoeff>::max()

Definition at line 43 of file kl.h.

const KLCoeff atlas::kl::UndefMuCoeff = std::numeric_limits<MuCoeff>::max()

Definition at line 44 of file kl.h.

const KLPol atlas::kl::Zero

Polynomial 0, which is stored as a vector of size 0. Definition at line 38 of file kl.h.

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