\section{atlas::tits::Tits\-Group Class Reference}
\label{classatlas_1_1tits_1_1TitsGroup}\index{atlas::tits::TitsGroup@{atlas::tits::TitsGroup}}
{\tt \#include $<$tits.h$>$}

Collaboration diagram for atlas::tits::Tits\-Group:\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[width=240pt]{classatlas_1_1tits_1_1TitsGroup__coll__graph}
\end{center}
\end{figure}
\subsection*{Public Member Functions}
\begin{CompactItemize}
\item 
{\bf Tits\-Group} ()
\item 
{\bf Tits\-Group} (const {\bf rootdata::Root\-Datum} \&, const {\bf latticetypes::Lattice\-Matrix} \&)
\item 
{\bf $\sim$Tits\-Group} ()
\item 
void {\bf conjugate} ({\bf Tits\-Elt} \&a, {\bf weyl::Generator} {\bf s}) const 
\item 
void {\bf inv\-Conjugate} ({\bf Torus\-Part} \&, const {\bf weyl::Weyl\-Elt} \&) const 
\item 
void {\bf left\-Prod} ({\bf Tits\-Elt} \&, {\bf weyl::Generator}) const 
\item 
unsigned long {\bf length} (const {\bf Tits\-Elt} \&a) const 
\item 
void {\bf prod} ({\bf Tits\-Elt} \&, {\bf weyl::Generator}) const 
\item 
void {\bf prod} ({\bf Tits\-Elt} \&, const {\bf Tits\-Elt} \&) const 
\item 
const size\_\-t {\bf rank} () const 
\item 
void {\bf reflection} ({\bf Torus\-Part} \&x, {\bf weyl::Generator} {\bf s}) const 
\item 
const {\bf Torus\-Part} \& {\bf simple\-Coroot} (size\_\-t j) const 
\item 
const {\bf Torus\-Part} \& {\bf simple\-Root} (size\_\-t j) const 
\item 
size\_\-t {\bf twist} (size\_\-t j) const 
\item 
void {\bf twisted\-Conjugate} ({\bf Tits\-Elt} \&a, {\bf weyl::Generator} {\bf s}) const 
\item 
const {\bf weyl::Weyl\-Group} \& {\bf weyl\-Group} () const 
\item 
void {\bf swap} ({\bf Tits\-Group} \&)
\end{CompactItemize}
\subsection*{Private Member Functions}
\begin{CompactItemize}
\item 
{\bf Tits\-Group} (const {\bf Tits\-Group} \&)
\item 
{\bf Tits\-Group} \& {\bf operator=} (const {\bf Tits\-Group} \&)
\end{CompactItemize}
\subsection*{Private Attributes}
\begin{CompactItemize}
\item 
{\bf weyl::Weyl\-Group} $\ast$ {\bf d\_\-weyl}
\item 
size\_\-t {\bf d\_\-rank}
\item 
std::vector$<$ {\bf Torus\-Part} $>$ {\bf d\_\-simple\-Root}
\item 
std::vector$<$ {\bf Torus\-Part} $>$ {\bf d\_\-simple\-Coroot}
\item 
{\bf Torus\-Matrix} {\bf d\_\-involution}
\item 
{\bf weyl::Twist} {\bf d\_\-twist}
\end{CompactItemize}


\subsection{Constructor \& Destructor Documentation}
\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!TitsGroup@{TitsGroup}}
\index{TitsGroup@{TitsGroup}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::tits::Tits\-Group::Tits\-Group (const {\bf Tits\-Group} \&)\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_33c53d594ea4782d634eb68e19bb544f}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!TitsGroup@{TitsGroup}}
\index{TitsGroup@{TitsGroup}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::tits::Tits\-Group::Tits\-Group ()\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_7668b0e232088fce6c95c2ceff87d979}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!TitsGroup@{TitsGroup}}
\index{TitsGroup@{TitsGroup}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::tits::Tits\-Group::Tits\-Group (const {\bf rootdata::Root\-Datum} \&, const {\bf latticetypes::Lattice\-Matrix} \&)}\label{classatlas_1_1tits_1_1TitsGroup_65baaf13434a3c1e2900042f2f511778}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!~TitsGroup@{$\sim$TitsGroup}}
\index{~TitsGroup@{$\sim$TitsGroup}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}atlas::tits::Tits\-Group::$\sim$Tits\-Group ()}\label{classatlas_1_1tits_1_1TitsGroup_51e33b761b93f03c8dfa495e43ff8084}




\subsection{Member Function Documentation}
\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!conjugate@{conjugate}}
\index{conjugate@{conjugate}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::conjugate ({\bf Tits\-Elt} \& {\em a}, {\bf weyl::Generator} {\em s}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_003cb1fdd2f31963b54abe330ef83043}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!invConjugate@{invConjugate}}
\index{invConjugate@{invConjugate}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::inv\-Conjugate ({\bf Torus\-Part} \&, const {\bf weyl::Weyl\-Elt} \&) const}\label{classatlas_1_1tits_1_1TitsGroup_cf4c814db66ada0247fadca3eb3f79d7}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!leftProd@{leftProd}}
\index{leftProd@{leftProd}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::left\-Prod ({\bf Tits\-Elt} \&, {\bf weyl::Generator}) const}\label{classatlas_1_1tits_1_1TitsGroup_2ab24d13bea8a0840f95f5d9db8e9283}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!length@{length}}
\index{length@{length}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}unsigned long atlas::tits::Tits\-Group::length (const {\bf Tits\-Elt} \& {\em a}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_ad3ddaecdf303770644e9d4d3a2ddd12}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!operator=@{operator=}}
\index{operator=@{operator=}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf Tits\-Group}\& atlas::tits::Tits\-Group::operator= (const {\bf Tits\-Group} \&)\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_4f9a8f7eff1558c9a1a89a156907f709}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!prod@{prod}}
\index{prod@{prod}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::prod ({\bf Tits\-Elt} \&, const {\bf Tits\-Elt} \&) const}\label{classatlas_1_1tits_1_1TitsGroup_190e957caf0c5189b133b823563a0949}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!prod@{prod}}
\index{prod@{prod}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::prod ({\bf Tits\-Elt} \&, {\bf weyl::Generator}) const}\label{classatlas_1_1tits_1_1TitsGroup_d81652bbe0da2700fca1b063ceb34478}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!rank@{rank}}
\index{rank@{rank}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const size\_\-t atlas::tits::Tits\-Group::rank () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_df08a3554b06bd83b378ae70131caf61}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!reflection@{reflection}}
\index{reflection@{reflection}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::reflection ({\bf Torus\-Part} \& {\em x}, {\bf weyl::Generator} {\em s}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_cfab7f11f4fd50a4f4bd19496041d341}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!simpleCoroot@{simpleCoroot}}
\index{simpleCoroot@{simpleCoroot}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf Torus\-Part}\& atlas::tits::Tits\-Group::simple\-Coroot (size\_\-t {\em j}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_a4fc567a6781923b965b6bd025c0a7ec}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!simpleRoot@{simpleRoot}}
\index{simpleRoot@{simpleRoot}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf Torus\-Part}\& atlas::tits::Tits\-Group::simple\-Root (size\_\-t {\em j}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_a45eb07379b5023b48be967cea79bf81}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!swap@{swap}}
\index{swap@{swap}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::swap ({\bf Tits\-Group} \&)}\label{classatlas_1_1tits_1_1TitsGroup_ae877135d4ba2bbea36ae0f058e939d2}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!twist@{twist}}
\index{twist@{twist}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t atlas::tits::Tits\-Group::twist (size\_\-t {\em j}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_83363b637657b25d9fa112849a3ed801}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!twistedConjugate@{twistedConjugate}}
\index{twistedConjugate@{twistedConjugate}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::tits::Tits\-Group::twisted\-Conjugate ({\bf Tits\-Elt} \& {\em a}, {\bf weyl::Generator} {\em s}) const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_88f1d0b0d2be92c73cc7acc78590c136}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!weylGroup@{weylGroup}}
\index{weylGroup@{weylGroup}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf weyl::Weyl\-Group}\& atlas::tits::Tits\-Group::weyl\-Group () const\hspace{0.3cm}{\tt  [inline]}}\label{classatlas_1_1tits_1_1TitsGroup_522053a115a3c70e0868936d986d97f3}




\subsection{Member Data Documentation}
\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_involution@{d\_\-involution}}
\index{d_involution@{d\_\-involution}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf Torus\-Matrix} {\bf atlas::tits::Tits\-Group::d\_\-involution}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_cde3bc70d919e1a525c1fcbe9cb588d5}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_rank@{d\_\-rank}}
\index{d_rank@{d\_\-rank}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}size\_\-t {\bf atlas::tits::Tits\-Group::d\_\-rank}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_4e27124bb614a2b58138380406cb246c}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_simpleCoroot@{d\_\-simpleCoroot}}
\index{d_simpleCoroot@{d\_\-simpleCoroot}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<${\bf Torus\-Part}$>$ {\bf atlas::tits::Tits\-Group::d\_\-simple\-Coroot}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_c24a65f141f7fba8bccf99f9077bc570}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_simpleRoot@{d\_\-simpleRoot}}
\index{d_simpleRoot@{d\_\-simpleRoot}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}std::vector$<${\bf Torus\-Part}$>$ {\bf atlas::tits::Tits\-Group::d\_\-simple\-Root}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_1031f0ba17e106ba131bfdfcb4e7ee20}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_twist@{d\_\-twist}}
\index{d_twist@{d\_\-twist}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf weyl::Twist} {\bf atlas::tits::Tits\-Group::d\_\-twist}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_ebfdf6b52736f2f8312f38a9a1fec1af}


\index{atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}!d_weyl@{d\_\-weyl}}
\index{d_weyl@{d\_\-weyl}!atlas::tits::TitsGroup@{atlas::tits::Tits\-Group}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf weyl::Weyl\-Group}$\ast$ {\bf atlas::tits::Tits\-Group::d\_\-weyl}\hspace{0.3cm}{\tt  [private]}}\label{classatlas_1_1tits_1_1TitsGroup_183ac19f891ddc3a7d34f22f0f4c1a9b}




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