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% $Id: GradedCombinatorialClass.tex,v 1.1.1.2 2004/10/05 17:12:08 nthiery Exp $
% File:		lib/DOMAINS/CATEGORY/DOC/GradedCombinatorialClass.tex
% Authors:	Florent Hivert <florent.hivert@univ-mlv.fr>
% Purpose:	Documentation for the category Cat::GradedCombinatorialClass
% Created:	Mon Feb 16 21:59:38 2004
% License:	LGPL
% Project:	MuPAD-Combinat, http://mupad-combinat.sf.net
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\begin{Mhelppage}{GradedCombinatorialClass}{Florent Hivert, Nicolas M. Thiéry}
  [ImplState=stable,TestState=beta,DocState=beta]
%\Mproofread{...}{...}{...}

\begin{MInfo}
  \eng{the category of graded combinatorial classes}
  \de{}
\end{MInfo}

\begin{MIntro}
  \eng{\Mthis{} represents the category of graded combinatorial classes.}
  \de{}
\end{MIntro}

\begin{MCatConst}
  \MCall{}
\end{MCatConst}

\begin{MCategories}
  \Mup{Cat::CombinatorialClass}
\end{MCategories}

\begin{MDetails}
  \eng{A \Mthis{} is a \Mup{Cat::CombinatorialClass} equipped with a
    grading. That is, each object in the combinatorial class has a
    size which is typically, but not necessarily, a non negative
    integer.}
  
  \eng{Such a class is typically infinite; calling the \Mex{list}
    method without arguments may yield unpredictable results. On the
    other hand, the existing methods like \Mex{list}, \Mex{count},
    \Mex{generator}, or \Mex{unrank} will accept a size as first
    argument.}
\end{MDetails}

\begin{MDomBasEntries}
  \MDomEntry{typeSize}
  \eng{A type for the size; by default \Mup{Type::NonNegInt}.}
\end{MDomBasEntries}

\begin{MMethodDetails}{size}
  \infoEng{size of an object (optional).}
  \infoDe{}
  \call{\Mtype{object} x}
  \eng{Returns the size of an object of the class.}
\end{MMethodDetails}

\begin{MExample}{ex-basic1}
  \eng{Integer partitions form a graded combinatorial class:}
  \begin{Mexin}
combinat::partitions::hasProp(Cat::GradedCombinatorialClass)
  \end{Mexin}
  \begin{Mexout}
                             TRUE
  \end{Mexout}
  \eng{the size of a partition being defined as the sum of its
    entries:}
  \begin{Mexin}
combinat::partitions::size([4, 3, 2])
  \end{Mexin}
  \begin{Mexout}
                               9
  \end{Mexout}
  \eng{We can thus ask for the number of partitions of size \Mex{9}:}
  \begin{Mexin}
combinat::partitions::count(9)
  \end{Mexin}
  \begin{Mexout}
                              30
  \end{Mexout}
\end{MExample}


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

\end{Mhelppage}

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