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\title[\texttt{Sage-Combinat},
  Free and Practical Software
  for Algebraic Combinatorics]{\texttt{Sage-Combinat}\\
  Free and Practical Software\\
  for Algebraic Combinatorics}

\author[{Nicolas M. Thiéry \textbf{et al.}}]{Nicolas M. Thiéry \textbf{et al.$^{1}$}}

\address{Department of Mathematics, University of California, One
 Shields Avenue, Davis, CA 95616, U.S.A.\\
 Univ Paris-Sud, Laboratoire de Mathématiques d'Orsay,
  Orsay, F-91405; CNRS, Orsay, F-91405, France}

%\email{Nicolas.Thiery@u-psud.fr}


\begin{document}


\maketitle

\section{Description}

\texttt{Sage}~\cite{Sage} (\url{http://www.sagemath.org}) is a free
open-source mathematics software system licensed under the GPL. It
combines the power of many existing open-source packages
(GAP~\cite{GAP4}, Linbox, Singular~\cite{Singular} to name a few) into
a common Python-based interface.

The mission of \texttt{Sage-Combinat} itself
(\texttt{http://wiki.sagemath.org/combinat/}) is to improve
\texttt{Sage} as an extensible toolbox for computer exploration in
combinatorics and algebraic combinatorics, and to foster code sharing
between researchers in this area.
%
As such, \texttt{Sage-Combinat} and its predecessor
\texttt{MuPAD-Combinat} played an essential role in more than 50
publications.

In practice, \texttt{Sage-Combinat} takes the form of a collection of
experimental extensions (patches), developed jointly by a growing
community of researchers\footnote{ Nicolas Borie, Jason Bandlow,
  Daniel Bump, Adrien Boussicault, Vincent Delecroix, Tom Denton,
  Teresa Gomez-Diaz, Mike Hansen, Florent Hivert, Brant Jones,
  Sébastien Labbé, Gregg Musiker, Franco Saliola, Anne Schilling, Mark
  Shimozono, Lenny Tevlin, Nicolas M. Thiéry, Justin Walker, Mike
  Zabrocki, as well as, for \texttt{MuPAD-Combinat} and sister
  projects, Houda Abbad, Christophe Carré, Frédéric Chapoton, François
  Descouens, Ralf Hemmecke, Éric Laugerotte, Cédric Lecouvey, Patrick
  Lemeur, Robert Miller, Xavier Molinero, Jean-Christophe Novelli,
  Janvier Nzeutchap, Wang Qiang, Martin Rubey }, worldwide. Those
extensions are intended to have a short life cycle, and to be merged
into the \texttt{Sage} library as soon as they are mature
enough. Hence, in a matter of months, most new features are made
available to all \texttt{Sage} users. Those interested in the bleeding
edge features can further download the experimental extensions by
simply running \texttt{Sage} as \texttt{sage -combinat install}.


\section{Software demonstration}
  
During the software demonstration at FPSAC'09, we will present the
prominent features of \texttt{Sage} for combinatorics and algebraic
combinatorics, and discuss its design and development
model. Afterward, we will run some informal tutorials during the
evenings. For those interested
in learning more or getting involved, there will also be a satellite
workshop around \texttt{Sage-Combinat} and sister projects:

\noindent
\texttt{*-Combinat 09}\\
July 25-29, RISC, Linz, Austria\\
Free and Practical Software for Algebraic Combinatorics\\
\url{http://wiki.sagemath.org/combinat/fpsac09}.


\section{Short history of \texttt{*-Combinat}}

\texttt{Sage-Combinat} started in 2000, under the name
\texttt{MuPAD-Combinat}~\cite{Hivert_Thiery.MuPAD-Combinat.2004}, as
an open source library for the computer algebra system
\texttt{MuPAD}~\cite{MuPAD.96}. It took its roots in the projects
\texttt{ACE}~\cite{ACE}, $\mu$\texttt{-EC}~\cite{muEC},
\texttt{PerMuVAR}~\cite{Thiery.PerMuVAR}, and progressively integrated
\texttt{CS}~\cite{Denise_all.1998.CS},
\texttt{Symmetrica}~\cite{SYMMETRICA}
\texttt{Nauty}~\cite{McKay.nauty} and \texttt{lrcalc}. The
\texttt{MuPAD} platform was technically sound, and played its role
very well for the first seven years. However, and as it was clear from
the beginning, it suffered from not being open source. In particular,
this hindered its dissemination, and the growth opportunities for both
the users and developers community. This motivated our decision, in
June 2008, to migrate the project to \texttt{Sage}, once this platform
became mature enough, and despite the large overhead (100k lines of
code to migrate). This migration allowed to almost double the
community, in particular thanks to joining our efforts with the
combinatorics on words project \texttt{Sage-words}.

The migration is on its way, and it is expected that, by FPSAC'09,
most of the combinatorics code will be migrated, as well as part of
the algebraic code.


%(Marne-la-Vallée, Rouen, Orsay, Barcelone, UC-Davis, Stanford,
%Toronto, Philadelphie, Seattle, ...).


\section{Features}
\label{section.sage}

From \url{http://www.sagemath.org/tour.html}:

\texttt{Sage} can be used to study general and advanced, pure and
applied mathematics. This comprises a wide range of mathematics,
including algebra, calculus, elementary to very advanced number
theory, cryptography, numerical computation, commutative algebra,
group theory, combinatorics, graph theory, exact linear algebra and
much more. It combines various software packages and seamlessly
integrates their functionality into a common experience. It is well
suited for education, studying and research.  The interface is a
notebook in a web-browser or the command-line. Using the notebook,
Sage connects either locally to your own Sage installation or to a
Sage server on the network. Inside the Sage notebook you can create
embedded graphics, beautifully typeset mathematical expressions, add
and delete input, and share your work across the network.

Here are some of the features of \texttt{Sage} that are developed
specifically by the \texttt{Sage-Combinat} project:
\begin{itemize}
\item Basic combinatorial classes: permutations, tableaux, ...
\item Decomposable objects / Species
\item Root systems and crystals
\item Combinatorics on words
\item (Non commutative) symmetric functions and related combinatorial
  (Hopf) algebras
\item Easy definitions of new combinatorial (Hopf) algebras
\end{itemize}

Other \texttt{Sage} features related to combinatorics include graphs
(in particular via \texttt{NetworkX}), groups (via \texttt{GAP}), etc.

\section{Hardware requirements}

\texttt{Sage} can be installed on most platforms, including
\texttt{Linux}, \texttt{Mac OS X}, and \texttt{Windows}.

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