\section{atlas::kgb::KGB Class Reference}
\label{classatlas_1_1kgb_1_1KGB}\index{atlas::kgb::KGB@{atlas::kgb::KGB}}
{\tt \#include $<$kgb.h$>$}

Collaboration diagram for atlas::kgb::KGB:\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[width=248pt]{classatlas_1_1kgb_1_1KGB__coll__graph}
\end{center}
\end{figure}
\subsection*{Public Member Functions}
\begin{CompactItemize}
\item 
{\bf KGB} (size\_\-t)
\item 
{\bf KGB} ({\bf realredgp::Real\-Reductive\-Group} \&)
\item 
virtual {\bf $\sim$KGB} ()
\item 
void {\bf swap} ({\bf KGB} \&)
\item 
const {\bf bruhat::Bruhat\-Order} \& {\bf bruhat\-Order} () const 
\item 
{\bf KGBElt} {\bf cayley} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
bool {\bf compare} ({\bf KGBElt}, {\bf KGBElt}) const 
\item 
{\bf KGBElt} {\bf cross} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
const {\bf Descent} \& {\bf descent} ({\bf KGBElt} x) const 
\item 
{\bf KGBElt\-Pair} {\bf inverse\-Cayley} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
bool {\bf is\-Ascent} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
bool {\bf is\-Descent} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
size\_\-t {\bf length} ({\bf KGBElt} x) const 
\item 
size\_\-t {\bf rank} () const 
\item 
size\_\-t {\bf size} () const 
\item 
const {\bf gradings::Status} \& {\bf status} ({\bf KGBElt} x) const 
\item 
{\bf gradings::Status::Value} {\bf status} (size\_\-t {\bf s}, {\bf KGBElt} x) const 
\item 
const {\bf weyl::Weyl\-Elt} \& {\bf involution} ({\bf KGBElt}) const 
\item 
{\bf KGBElt\-Pair} {\bf tau\-Packet} (const {\bf weyl::Weyl\-Elt} \&) const 
\item 
const {\bf weyl::Weyl\-Group} \& {\bf weyl\-Group} () const 
\item 
size\_\-t {\bf weyl\-Length} ({\bf KGBElt}) const 
\item 
void {\bf fill\-Bruhat} ()
\end{CompactItemize}
\subsection*{Protected Types}
\begin{CompactItemize}
\item 
enum {\bf State} \{ {\bf Bruhat\-Constructed}, 
{\bf Num\-States}
 \}
\end{CompactItemize}
\subsection*{Protected Attributes}
\begin{CompactItemize}
\item 
size\_\-t {\bf d\_\-rank}
\item 
std::vector$<$ {\bf KGBElt\-List} $>$ {\bf d\_\-cross}
\item 
std::vector$<$ {\bf KGBElt\-List} $>$ {\bf d\_\-cayley}
\item 
std::vector$<$ {\bf KGBElt\-Pair\-List} $>$ {\bf d\_\-inverse\-Cayley}
\item 
{\bf Descent\-List} {\bf d\_\-descent}
\item 
std::vector$<$ size\_\-t $>$ {\bf d\_\-length}
\item 
{\bf weyl::Weyl\-Elt\-List} {\bf d\_\-involution}
\item 
{\bf gradings::Status\-List} {\bf d\_\-status}
\item 
{\bf bitset::Bit\-Set}$<$ Num\-States $>$ {\bf d\_\-state}
\item 
{\bf bruhat::Bruhat\-Order} $\ast$ {\bf d\_\-bruhat}
\item 
const {\bf weyl::Weyl\-Group} $\ast$ {\bf d\_\-weyl\-Group}
\end{CompactItemize}


\subsection{Member Enumeration Documentation}
\index{atlas::kgb::KGB@{atlas::kgb::KGB}!State@{State}}
\index{State@{State}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}enum {\bf atlas::kgb::KGB::State}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_aef27c6d342e9b5e8e2064909c4d955d}


\begin{Desc}
\item[Enumerator: ]\par
\begin{description}
\index{BruhatConstructed@{BruhatConstructed}!atlas::kgb::KGB@{atlas::kgb::KGB}}\index{atlas::kgb::KGB@{atlas::kgb::KGB}!BruhatConstructed@{BruhatConstructed}}\item[{\em 
Bruhat\-Constructed\label{classatlas_1_1kgb_1_1KGB_aef27c6d342e9b5e8e2064909c4d955d5754c478b88caa8a58de4040817d1ff6}
}]\index{NumStates@{NumStates}!atlas::kgb::KGB@{atlas::kgb::KGB}}\index{atlas::kgb::KGB@{atlas::kgb::KGB}!NumStates@{NumStates}}\item[{\em 
Num\-States\label{classatlas_1_1kgb_1_1KGB_aef27c6d342e9b5e8e2064909c4d955d86eae5b397a4d3ce350cb3c44f3fb080}
}]\end{description}
\end{Desc}



\subsection{Constructor \& Destructor Documentation}
\index{atlas::kgb::KGB@{atlas::kgb::KGB}!KGB@{KGB}}
\index{KGB@{KGB}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::kgb::KGB::KGB (size\_\-t)\hspace{0.3cm}{\tt  [explicit]}}\label{classatlas_1_1kgb_1_1KGB_5606be30caf4fae3aac71f18441d3cef}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!KGB@{KGB}}
\index{KGB@{KGB}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::kgb::KGB::KGB ({\bf realredgp::Real\-Reductive\-Group} \&)\hspace{0.3cm}{\tt  [explicit]}}\label{classatlas_1_1kgb_1_1KGB_983c132f9d521c22273bbd48d33b62eb}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!~KGB@{$\sim$KGB}}
\index{~KGB@{$\sim$KGB}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::kgb::KGB::$\sim$KGB ()\hspace{0.3cm}{\tt  [virtual]}}\label{classatlas_1_1kgb_1_1KGB_f2e489ceeb29e4298a6d49ee34a77006}




\subsection{Member Function Documentation}
\index{atlas::kgb::KGB@{atlas::kgb::KGB}!bruhatOrder@{bruhatOrder}}
\index{bruhatOrder@{bruhatOrder}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf bruhat::Bruhat\-Order}\& atlas::kgb::KGB::bruhat\-Order () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_b3a928059a2eee451cec7558387be450}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!cayley@{cayley}}
\index{cayley@{cayley}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf KGBElt} atlas::kgb::KGB::cayley (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_800af294cb7e5516e83864702d927640}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!compare@{compare}}
\index{compare@{compare}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}bool atlas::kgb::KGB::compare ({\bf KGBElt}, {\bf KGBElt}) const}\label{classatlas_1_1kgb_1_1KGB_454ba0b38dc43ee5efdf847eecae1857}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!cross@{cross}}
\index{cross@{cross}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf KGBElt} atlas::kgb::KGB::cross (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_3b62aa848f1128bb9eeaa89c065c3fd4}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!descent@{descent}}
\index{descent@{descent}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf Descent}\& atlas::kgb::KGB::descent ({\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_876795030f5f6b6d2f8701069f91adc3}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!fillBruhat@{fillBruhat}}
\index{fillBruhat@{fillBruhat}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::kgb::KGB::fill\-Bruhat ()}\label{classatlas_1_1kgb_1_1KGB_4db6f99c972e7771d262154de4b54391}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!inverseCayley@{inverseCayley}}
\index{inverseCayley@{inverseCayley}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf KGBElt\-Pair} atlas::kgb::KGB::inverse\-Cayley (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_074706b77dedb1226c6123cdadafcce2}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!involution@{involution}}
\index{involution@{involution}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf weyl::Weyl\-Elt} \& atlas::kgb::KGB::involution ({\bf KGBElt}) const}\label{classatlas_1_1kgb_1_1KGB_b3447e97a2bb1337be6704b1f8ad97a9}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!isAscent@{isAscent}}
\index{isAscent@{isAscent}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}bool atlas::kgb::KGB::is\-Ascent (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const}\label{classatlas_1_1kgb_1_1KGB_7469b4e54cdddc06dac7d1749c76b2fa}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!isDescent@{isDescent}}
\index{isDescent@{isDescent}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}bool atlas::kgb::KGB::is\-Descent (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const}\label{classatlas_1_1kgb_1_1KGB_4c332f52f0619e72a419c0aedb5b9468}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!length@{length}}
\index{length@{length}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t atlas::kgb::KGB::length ({\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_20c8e3d860b943969cc4dc0aa6b94638}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!rank@{rank}}
\index{rank@{rank}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t atlas::kgb::KGB::rank () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_668a535bc9bd099923725bf31f55fbbd}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!size@{size}}
\index{size@{size}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t atlas::kgb::KGB::size () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_25ae46eded6839bdb1f55af248383dc6}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!status@{status}}
\index{status@{status}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf gradings::Status::Value} atlas::kgb::KGB::status (size\_\-t {\em s}, {\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_e0caf527947c53bec1b339df6815f2ce}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!status@{status}}
\index{status@{status}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf gradings::Status}\& atlas::kgb::KGB::status ({\bf KGBElt} {\em x}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_5e2ffa5e73af88c29a58c8aa34fd41e6}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!swap@{swap}}
\index{swap@{swap}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::kgb::KGB::swap ({\bf KGB} \&)}\label{classatlas_1_1kgb_1_1KGB_fb214d7d4b656d934035756fc087edee}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!tauPacket@{tauPacket}}
\index{tauPacket@{tauPacket}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf KGBElt\-Pair} atlas::kgb::KGB::tau\-Packet (const {\bf weyl::Weyl\-Elt} \&) const}\label{classatlas_1_1kgb_1_1KGB_7571fe1b9520a073ce70d871027f9de7}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!weylGroup@{weylGroup}}
\index{weylGroup@{weylGroup}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf weyl::Weyl\-Group}\& atlas::kgb::KGB::weyl\-Group () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1kgb_1_1KGB_9152cd5c026c0cd01c60996c8fd8fd16}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!weylLength@{weylLength}}
\index{weylLength@{weylLength}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t atlas::kgb::KGB::weyl\-Length ({\bf KGBElt}) const}\label{classatlas_1_1kgb_1_1KGB_2b4d5b33238fba169a4f4a53167e969e}




\subsection{Member Data Documentation}
\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_bruhat@{d\_\-bruhat}}
\index{d_bruhat@{d\_\-bruhat}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf bruhat::Bruhat\-Order}$\ast$ {\bf atlas::kgb::KGB::d\_\-bruhat}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_fe2fcd15162a4a67eb5b65667d2bb5a5}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_cayley@{d\_\-cayley}}
\index{d_cayley@{d\_\-cayley}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<${\bf KGBElt\-List}$>$ {\bf atlas::kgb::KGB::d\_\-cayley}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_3c0b228839777291425e81d34b13ee6a}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_cross@{d\_\-cross}}
\index{d_cross@{d\_\-cross}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<${\bf KGBElt\-List}$>$ {\bf atlas::kgb::KGB::d\_\-cross}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_52a900793fc3c9ec4e860dd2259d8c8c}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_descent@{d\_\-descent}}
\index{d_descent@{d\_\-descent}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf Descent\-List} {\bf atlas::kgb::KGB::d\_\-descent}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_4b8b42d4b1ec5eb064f0037659ad927a}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_inverseCayley@{d\_\-inverseCayley}}
\index{d_inverseCayley@{d\_\-inverseCayley}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<${\bf KGBElt\-Pair\-List}$>$ {\bf atlas::kgb::KGB::d\_\-inverse\-Cayley}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_04f70f72942cafec016cbbc8caa63bc7}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_involution@{d\_\-involution}}
\index{d_involution@{d\_\-involution}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf weyl::Weyl\-Elt\-List} {\bf atlas::kgb::KGB::d\_\-involution}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_c58cf57489edbb8ec3e4c41cacf4d8bb}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_length@{d\_\-length}}
\index{d_length@{d\_\-length}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<$size\_\-t$>$ {\bf atlas::kgb::KGB::d\_\-length}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_7af834e4efdf4c0dd73325eefdb7b0c9}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_rank@{d\_\-rank}}
\index{d_rank@{d\_\-rank}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t {\bf atlas::kgb::KGB::d\_\-rank}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_4b605fc0f085deca73c40849c57fefdd}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_state@{d\_\-state}}
\index{d_state@{d\_\-state}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf bitset::Bit\-Set}$<$Num\-States$>$ {\bf atlas::kgb::KGB::d\_\-state}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_1e7722d6a9410a14c17cc2cc453d9689}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_status@{d\_\-status}}
\index{d_status@{d\_\-status}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf gradings::Status\-List} {\bf atlas::kgb::KGB::d\_\-status}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_963a6224606ec267e6bb253244f9a18f}


\index{atlas::kgb::KGB@{atlas::kgb::KGB}!d_weylGroup@{d\_\-weylGroup}}
\index{d_weylGroup@{d\_\-weylGroup}!atlas::kgb::KGB@{atlas::kgb::KGB}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf weyl::Weyl\-Group}$\ast$ {\bf atlas::kgb::KGB::d\_\-weyl\-Group}\hspace{0.3cm}{\tt  [protected]}}\label{classatlas_1_1kgb_1_1KGB_ead63b1025aaa81106a9778c25690356}




The documentation for this class was generated from the following files:\begin{CompactItemize}
\item 
sources/gkmod/{\bf kgb.h}\item 
sources/gkmod/{\bf kgb.cpp}\end{CompactItemize}
