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% $Id: countingFunctions.tex,v 1.1.1.2 2005/01/26 13:42:24 nthiery Exp $
% File:		lib/COMBINAT/DOC/countingFunctions.tex
% Authors:	Nicolas M. Thiéry <nthiery@users.sourceforge.net>
% Purpose:	Documentation for the domain combinat::countingFunctions
% Created:	Sat Jul  3 10:19:07 2004
% License:	LGPL
% Project:	MuPAD-Combinat, http://mupad-combinat.sf.net
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\begin{Mhelppage}{countingFunctions}{Nicolas M. Thiéry}
  [ImplState=alpha,TestState=beta,DocState=alpha]
%\Mproofread{...}{...}{proofread}

\begin{MInfo}
  \eng{counting functions}
  \de{}
\end{MInfo}

\begin{MIntro}
  \eng{A \emph{counting function} $f$ is a function from the non
    negative integers to themselves. Typically $f(n)$ counts the
    number of objects of size $n$ in a given graded combinatorial
    class. Otherwise said, $f(n)$ is the $n$-th coefficient of the
    generating series associated to the combinatorial class.}
  
  \eng{A \emph{functor} takes one or several counting functions and
    returns a new counting function. For example, if \emph{f} counts
    the objects of a combinatorial class $A$ the functor \emph{set}
    returns the counting function for the sets of objects of $A$. Most
    functors correspond similarly to operations on combinatorial
    classes or the corresponding generating series.}
  
  \eng{This library essentially provides classical functors for
    counting functions. Most of those functors actually work more
    generally with function from the non-negative integers to some
    ring.}
  
  \eng{This library is intended as a repository of fast low-level
    utilities. Higher level interfaces (say in the form of generating
    series) could be built upon it.}
\end{MIntro}

\begin{MMethodDetails}{mult2}
  \infoEng{multiplication of counting functions}
  \call{\Mtype{counting function} f, \Mtype{counting function} g}
  \eng{Returns the product \Mex{h} of \Mpar{f} and \Mpar{g},
    Namely $h(n)=\sum^n_{k=0} f(k) g(n-k)$.}
  \eng{This corresponds to the Cartesian product of graded
    combinatorial class, or the product of generating series.}
\end{MMethodDetails}

\begin{MChanges}
  \version{3.1}
  \eng[New domain]{\Mthis{} is a new domain} %
\end{MChanges}

\end{Mhelppage}
