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\title{The REDUCE package SSTOOLS \\
       **** Preliminary Documentation ***}
\author{Thomas Wolf \\                        
        Department of Mathematics \\
        Brock University \\
        St.Catharines \\
        Ontario, Canada L2S 3A1 \\
        twolf@brocku.ca \\
        \\
        Eberhard Schruefer \\
        eschruefer@ca-musings.de}

\begin{document}
\maketitle
\section{Purpose}
{\tt SSTOOLS} is a collection of procedures
that facilitates computations with supersymmetric algebraic and differential
expressions.

\section{Overview}
A detailed description is available through the online tutorial \\
{\tt https://lie.ac.brocku.ca/crack/susy/}. An essentially equivalent 
description is available after loading {\sc SsTools} and issuing the command
{\tt sshelp()\$}. The correct functioning of all procedures is tested through
reading in and running {\tt sstools.tst}. This test also illustrates
the commutator rules for products of the different fields and their
derivatives with respect to besonic and fermionic variables.

The topics in the tutorial and in {\tt sshelp()\$} are:
\begin{description} \itemsep -3pt
\item{Purpose}
\item{Interactive Session}
\item{Loading Files}
\item{Notation}
\item{Initializations}
\item{The command coeffn}
\item{The procedure SSym}
\item{The procedure SSConL}
\item{The procedure FindSSWeights}
\item{The procedure Linearize}
\item{The procedure GenSSPoly}
\item{The procedure ToCoo}
\item{The procedure ToField}
\item{Discovery of recursion operators}
\item{Verification of symmetries}
\end{description}

%\section{Requirements}
%{\sc Reduce} version ID 3500 or higher from April 5, 2016 or later,
%and the package {\sc Crack} in a version that comes with {\sc Reduce}.
%If {\sc Crack} is downloaded from \\
%{\tt http://lie.math.brocku.ca/crack/src/crack.tar.gz} then 
%one does \\
%\verb+    IN "crack.red"$+ \\
%(and appropriate paths) or compilation with \\
%\verb+    FASLOUT "crack"$+ \\
%\verb+    IN "crack.red"$+ \\
%\verb+    FASLEND$+ \\
%\verb+    BYE$+ \\
%and loads {\sc Crack} afterwards with \verb+ LOAD_PACKAGE crack$.+

\begin{thebibliography}{99}

\bibitem{bi1}
Hussin, V., Kiselev, A.V., Krutov, A.O., Wolf, T.: N=2 Supersymmetric a=4 -
Korteweg-de Vries hierarchy derived via Gardner's deformation of
Kaup-Bousinesq equation, J. Math. Phys. 51, 083507 (2010);
doi:10.1063/1.3447731 (19 pages) link, pdf file

\bibitem{bi2}
Kiselev, A. and Wolf, T.: Supersymmetric Representations and Integrable
Super-Extensions of the Burgers and Bussinesq Equations, SIGMA, Vol. 2 (2006),
Paper 030, 19 pages (arXiv math-ph/0511071). ps file, pdf file

\bibitem{bi3}
Kiselev, A. and Wolf, T.: On weakly non-local, nilpotent, and super-recursion
operators for N=1 homogeneous super-equations, Proc. Int. Workshop
``Supersymmetries and Quantum Symmetries'' (SQS'05), Dubna, July 24--31, 2005,
JINR, p. 231--237. (arXiv nlin.SI/0511056)
http://theor.jinr.ru/~sqs05/SQS05.pdf dvi file, ps file,

\bibitem{bi4}
Kiselev, A. and Wolf, T.: Classification of integrable super-equations by the
SsTools environment, Comp Phys Comm, Vol. 177, no. 3 (2007) p 315-328 (and on
arXiv: nlin.SI/0609065). dvi file, ps file, pdf file

\bibitem{bi5}
I. S. Krasil'shchik, P. H. M. Kersten, Symmetries and recursion operators for
classical and supersymmetric differential equations, Kluwer Acad. Publ.,
Dordrecht etc, (2000) 

\end{thebibliography}

\end{document}
