atlas  0.6
atlas::kl Namespace Reference

## Classes

class  KLContext

class  KLPolEntry

## Typedefs

typedef unsigned int KLCoeff

typedef polynomials::Safe_Poly< KLCoeffKLPol

typedef unsigned int KLIndex

typedef KLCoeff MuCoeff

typedef std::vector< KLPolKLStore

typedef KLStore::const_reference KLPolRef

typedef std::vector< KLIndexKLRow

typedef std::vector< BlockEltPrimitiveRow

typedef std::vector< std::pair< BlockElt, MuCoeff > > MuRow

## Functions

void wGraph (wgraph::WGraph &wg, const KLContext &klc)
Puts in wg the W-graph for this block. More...

## Variables

const KLPol Zero
Polynomial 0, which is stored as a vector of size 0. More...

const KLPol One (0, KLCoeff(1))
Polynomial 1.q^0. More...

## Typedef Documentation

 typedef unsigned int atlas::kl::KLCoeff
 typedef unsigned int atlas::kl::KLIndex
 typedef KLStore::const_reference atlas::kl::KLPolRef
 typedef std::vector atlas::kl::KLRow
 typedef std::vector atlas::kl::KLStore
 typedef KLCoeff atlas::kl::MuCoeff
 typedef std::vector > atlas::kl::MuRow
 typedef std::vector atlas::kl::PrimitiveRow

## Function Documentation

 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.

## Variable Documentation

 const KLPol atlas::kl::One(0, KLCoeff(1))

Polynomial 1.q^0.

 const KLPol atlas::kl::Zero

Polynomial 0, which is stored as a vector of size 0.