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% $Id: GradedAlgebraWithBasis.tex,v 1.1.1.3 2004/10/04 17:25:13 nthiery Exp $
% File:		lib/DOMAINS/CATEGORY/DOC/GradedAlgebraWithBasis.tex
% Authors:	Nicolas M. Thiéry <nthiery@users.sourceforge.net>
% Purpose:	Documentation for the category Cat::GradedAlgebraWithBasis
% Created:	Wed Sep  3 14:48:23 2003
% License:	LGPL
% Project:	MuPAD-Combinat, http://mupad-combinat.sf.net
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{Mhelppage}{GradedAlgebraWithBasis}{Nicolas M. Thiéry}
  [ImplState=stable,TestState=stable,DocState=stable]
%\Mproofread{...}{...}{...}

\begin{MInfo}
  \eng{the category of graded algebras over a distinguished basis}
  \de{}
\end{MInfo}

\Mproofread{nthiery}{22/09/2003}{minimal definition; not proofread}
\begin{MIntro}
  \eng{\Mthis{} represents the category of graded algebras over a
    distinguished basis.}
  \de{}
\end{MIntro}

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

\begin{MCategories}
  \Mupc{Cat::AlgebraWithBasis}{R}
  \Mupc{Cat::GradedModuleWithBasis}{R}
\end{MCategories}

\begin{MDetails}
  \eng{A \Mthis{} is an algebra over a distinguished basis
    (\Mup{Cat::AlgebraWithBasis}), with a grading which is compatible
    with the algebra operations and such that the basis elements are
    homogeneous (\Mup{Cat::GradedModuleWithBasis}).}
  \de{}
\end{MDetails}

\begin{MMethodDetails}{expTruncated}
  \infoEng{truncated exponential}
  \infoDe{}
  \call{\Mtype{dom} x, \Mtype{degree} order}
  \eng{Returns the exponential of \Mpar{x}, truncated to the order
    \Mpar{order}.}
\end{MMethodDetails}

\begin{MMethodDetails}{logTruncated}
  \infoEng{truncated logarithm}
  \infoDe{}
  \call{\Mtype{dom} x, \Mtype{degree} order}
  \eng{Returns the logarithm of \Mpar{x}, truncated to the order
    \Mpar{order}.}
\end{MMethodDetails}

\begin{MChanges}
  \version{3.0}
  \eng[New category]{\Mthis{} is a new category} %
\end{MChanges}

\end{Mhelppage}
