% from 18.3.1992 hk
% user packages, existing undocumented, planned


\section{Other Packages} % -----------------------------------------

In this section we list other important packages 
with only minimal descriptions. 


\subsection{Greatest common divisors and resultants} %----------

This package is from the original ALDES/SAC-2 
greatest common divisor and resultant package. 
It contains algorithms as described in \cite{Collins73} and 
the references given there. 
The programs are contained in the Modula-2 library 
\verb/SACPGCD/. 


\subsection{Polynomial factorization} %----------

This package is from the original ALDES/SAC-2 
polynomial factorization package. 
It contains algorithms as described in \cite{Collins73} and 
the references given there. 
The programs are contained in the Modula-2 libraries 
\verb/SACUPFAC/, \verb/SACMUFAC/ and \verb/SACPFAC/. 


\subsection{Polynomial real root isolation} %----------

This package is from the original ALDES/SAC-2 
univariate polynomial real root isolation package. 
It contains algorithms as described in \cite{CoL82} and 
the references given there. 
The programs are contained in the Modula-2 libraries 
\verb/SACROOT/ and in some of the \verb/SACEXT*/ libraries. 


\subsection{Symmetric functions} %----------

This package contains programs for the 
reduction of polynomials with respect to 
the elementary symmetric functions. 
By this reduction method it is possible to
decide if a given polynomial can be expressed in terms of the the 
elementary symmetric functions 
and also to determine such a representation.
The algorithms have been developed during a seminar 
of V. Weispfenning in Passau 1990. 
The programs are contained in the Modula-2 library
\verb/SYMMFU/.


\subsection{Linear algebra} %----------

This is a standard linear algebra package, which 
contains programs for 
Gaussian LU-decomposition, determination of special solutions 
of inhomogeneous systems of linear equations, 
determination of bases for the `nullspace' 
(solutions of the homogeneous system of equations).
Further functions contained are matrix multiplication, 
transposition, rang, determinants and input / output. 
The programs are written for matricies over 
the rational numbers and over the integers. 
The programs are contained in the Modula-2 libraries 
\verb/LINALGI/ and \verb/LINALGRN/. 


\subsection{Linear diophantine equations} %----------

This package is from the original ALDES/SAC-2 
linear diophantine equation package. 
It contains algorithms as described in \cite{CC82} 
and the references given there. 
The programs are contained in the Modula-2 libraries 
\verb/SACLINDIO/. 


\subsection{Non-Noetherian polynomial rings} %----------

The solvable polynomial rings introduced earlier are examples 
of non-commutative rings, which are still Noetherian 
(every (left, right) ideal is finitely generated).
General non-commutative polynomial rings are known to be 
no more Noetherian. Nevertheless there is a class of 
polynomial rings for which there exist finite Gr\"obner bases 
for finitely generated ideals.
The package contains algorithms as described in \cite{Bader94} 
and the references given there. 
The programs are contained in the Modula-2 libraries 
\verb/DINNG/. 


%\section{Planned Packages} % ------------------------------------------
%
%In this section we list some packages which are under 
%development and will be available in some time.
%

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