\section{atlas::abelian Namespace Reference}
\label{namespaceatlas_1_1abelian}\index{atlas::abelian@{atlas::abelian}}


\subsection*{Classes}
\begin{CompactItemize}
\item 
class {\bf Finite\-Abelian\-Group}
\item 
class {\bf Homomorphism}
\end{CompactItemize}
\subsection*{Typedefs}
\begin{CompactItemize}
\item 
typedef {\bf matrix::Matrix}$<$ unsigned long $>$ {\bf Endomorphism}
\item 
typedef unsigned long {\bf Grp\-Nbr}
\item 
typedef std::vector$<$ {\bf Grp\-Nbr} $>$ {\bf Grp\-Nbr\-List}
\item 
typedef std::vector$<$ unsigned long $>$ {\bf Grp\-Arr}
\item 
typedef std::vector$<$ {\bf Grp\-Arr} $>$ {\bf Grp\-Arr\-List}
\item 
typedef std::vector$<$ unsigned long $>$ {\bf Group\-Type}
\item 
typedef {\bf matrix::Matrix}$<$ unsigned long $>$ {\bf Endomorphism}
\end{CompactItemize}
\subsection*{Functions}
\begin{CompactItemize}
\item 
void {\bf basis} ({\bf latticetypes::Weight\-List} \&b, const {\bf bitmap::Bit\-Map} \&B, const {\bf Finite\-Abelian\-Group} \&A)
\item 
void {\bf coset} ({\bf bitmap::Bit\-Map} \&C, const {\bf bitmap::Bit\-Map} \&B, {\bf Grp\-Nbr} x, const {\bf Finite\-Abelian\-Group} \&A)
\item 
const {\bf bitmap::Bit\-Map} \& {\bf cyc\-Generators} (const {\bf Finite\-Abelian\-Group} \&A)
\item 
void {\bf generate\-Subgroup} ({\bf bitmap::Bit\-Map} \&B, {\bf Grp\-Nbr} x, const {\bf Finite\-Abelian\-Group} \&A)
\item 
void {\bf generators} ({\bf Grp\-Nbr\-List} \&gen, const {\bf bitmap::Bit\-Map} \&B, const {\bf Finite\-Abelian\-Group} \&A)
\item 
bool {\bf is\-Elementary\-Abelian} (const std::vector$<$ unsigned long $>$ \&c)
\item 
void {\bf quot\-Reps} ({\bf bitmap::Bit\-Map} \&qr, const {\bf bitmap::Bit\-Map} \&B, const {\bf Finite\-Abelian\-Group} \&A)
\item 
void {\bf to\-Array} ({\bf Grp\-Arr} \&a, {\bf Grp\-Nbr} x, const {\bf Group\-Type} \&t)
\item 
void {\bf to\-Array} ({\bf Grp\-Arr} \&a, const {\bf latticetypes::Weight} \&v, const {\bf Group\-Type} \&t)
\item 
void {\bf to\-Endomorphism} ({\bf Endomorphism} \&e, const {\bf latticetypes::Lattice\-Matrix} \&q, const {\bf Finite\-Abelian\-Group} \&A)
\item 
{\bf Grp\-Nbr} {\bf to\-Grp\-Nbr} (const {\bf Grp\-Arr} \&a, const {\bf Group\-Type} \&t)
\item 
void {\bf transpose} ({\bf Endomorphism} \&e, const {\bf Finite\-Abelian\-Group} \&A)
\end{CompactItemize}


\subsection{Typedef Documentation}
\index{atlas::abelian@{atlas::abelian}!Endomorphism@{Endomorphism}}
\index{Endomorphism@{Endomorphism}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef {\bf matrix::Matrix}$<$unsigned long$>$ {\bf atlas::abelian::Endomorphism}}\label{namespaceatlas_1_1abelian_5c4dcd1c19458e7b24edb7aab82343c6}


\index{atlas::abelian@{atlas::abelian}!Endomorphism@{Endomorphism}}
\index{Endomorphism@{Endomorphism}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef {\bf matrix::Matrix}$<$unsigned long$>$ {\bf atlas::abelian::Endomorphism}}\label{namespaceatlas_1_1abelian_5c4dcd1c19458e7b24edb7aab82343c6}


\index{atlas::abelian@{atlas::abelian}!GroupType@{GroupType}}
\index{GroupType@{GroupType}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef std::vector$<$unsigned long$>$ {\bf atlas::abelian::Group\-Type}}\label{namespaceatlas_1_1abelian_8a3a6c8121d843828cdec56e0139b826}


\index{atlas::abelian@{atlas::abelian}!GrpArr@{GrpArr}}
\index{GrpArr@{GrpArr}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef std::vector$<$unsigned long$>$ {\bf atlas::abelian::Grp\-Arr}}\label{namespaceatlas_1_1abelian_d457a581cf4d41d9680ce0ee44c70ecf}


\index{atlas::abelian@{atlas::abelian}!GrpArrList@{GrpArrList}}
\index{GrpArrList@{GrpArrList}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef std::vector$<${\bf Grp\-Arr}$>$ {\bf atlas::abelian::Grp\-Arr\-List}}\label{namespaceatlas_1_1abelian_94ee67347bf28d14f7ae49a81ade36c4}


\index{atlas::abelian@{atlas::abelian}!GrpNbr@{GrpNbr}}
\index{GrpNbr@{GrpNbr}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef unsigned long {\bf atlas::abelian::Grp\-Nbr}}\label{namespaceatlas_1_1abelian_68b66afefef6fe1240dde82aff7be1d3}


\index{atlas::abelian@{atlas::abelian}!GrpNbrList@{GrpNbrList}}
\index{GrpNbrList@{GrpNbrList}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}typedef std::vector$<${\bf Grp\-Nbr}$>$ {\bf atlas::abelian::Grp\-Nbr\-List}}\label{namespaceatlas_1_1abelian_7b056e41db578caeea19d8242128f25c}




\subsection{Function Documentation}
\index{atlas::abelian@{atlas::abelian}!basis@{basis}}
\index{basis@{basis}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::basis ({\bf latticetypes::Weight\-List} \& {\em b}, const bitmap::Bit\-Map \& {\em B}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_21a9ba4b1afc33dce173933de6d525cf}


\index{atlas::abelian@{atlas::abelian}!coset@{coset}}
\index{coset@{coset}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::coset (bitmap::Bit\-Map \& {\em C}, const bitmap::Bit\-Map \& {\em B}, {\bf Grp\-Nbr} {\em x}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_08052d50afb4c1ed89f9bbd4eab7772d}


\index{atlas::abelian@{atlas::abelian}!cycGenerators@{cycGenerators}}
\index{cycGenerators@{cycGenerators}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}const {\bf bitmap::Bit\-Map} \& atlas::abelian::cyc\-Generators (const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_06e9c3c736d2124c041ad073e8ed1014}


\index{atlas::abelian@{atlas::abelian}!generateSubgroup@{generateSubgroup}}
\index{generateSubgroup@{generateSubgroup}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::generate\-Subgroup (bitmap::Bit\-Map \& {\em B}, {\bf Grp\-Nbr} {\em x}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_20453ae10b1bc181c42f6e9eff4653ff}


\index{atlas::abelian@{atlas::abelian}!generators@{generators}}
\index{generators@{generators}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::generators ({\bf Grp\-Nbr\-List} \& {\em gen}, const bitmap::Bit\-Map \& {\em B}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_73596e57fd7535bf1a6c4488fa8412fa}


\index{atlas::abelian@{atlas::abelian}!isElementaryAbelian@{isElementaryAbelian}}
\index{isElementaryAbelian@{isElementaryAbelian}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}bool atlas::abelian::is\-Elementary\-Abelian (const std::vector$<$ unsigned long $>$ \& {\em c})}\label{namespaceatlas_1_1abelian_02fc62d7e3dcd3210814230c81cbf95a}


\index{atlas::abelian@{atlas::abelian}!quotReps@{quotReps}}
\index{quotReps@{quotReps}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::quot\-Reps (bitmap::Bit\-Map \& {\em qr}, const bitmap::Bit\-Map \& {\em B}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_e705b4b30163a10f8b07236d195a0655}


\index{atlas::abelian@{atlas::abelian}!toArray@{toArray}}
\index{toArray@{toArray}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::to\-Array ({\bf Grp\-Arr} \& {\em a}, const {\bf latticetypes::Weight} \& {\em v}, const {\bf Group\-Type} \& {\em t})}\label{namespaceatlas_1_1abelian_7c6c9451f04b10e4e21ca0297c9efcfa}


\index{atlas::abelian@{atlas::abelian}!toArray@{toArray}}
\index{toArray@{toArray}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::to\-Array ({\bf Grp\-Arr} \& {\em a}, {\bf Grp\-Nbr} {\em x}, const {\bf Group\-Type} \& {\em t})}\label{namespaceatlas_1_1abelian_09ea882a122f785e22ae48f3ab9e1f99}


\index{atlas::abelian@{atlas::abelian}!toEndomorphism@{toEndomorphism}}
\index{toEndomorphism@{toEndomorphism}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::to\-Endomorphism ({\bf Endomorphism} \& {\em e}, const {\bf latticetypes::Lattice\-Matrix} \& {\em q}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_af1cb443d2b014dfbdae6f34db081fbb}


\index{atlas::abelian@{atlas::abelian}!toGrpNbr@{toGrpNbr}}
\index{toGrpNbr@{toGrpNbr}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf Grp\-Nbr} atlas::abelian::to\-Grp\-Nbr (const {\bf Grp\-Arr} \& {\em a}, const {\bf Group\-Type} \& {\em t})}\label{namespaceatlas_1_1abelian_813ff4a643d6c45f79db3677a2e73c49}


\index{atlas::abelian@{atlas::abelian}!transpose@{transpose}}
\index{transpose@{transpose}!atlas::abelian@{atlas::abelian}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void atlas::abelian::transpose ({\bf Endomorphism} \& {\em e}, const Finite\-Abelian\-Group \& {\em A})}\label{namespaceatlas_1_1abelian_78cd49965f0f334bb496cf27cf49568b}


