    
                      SIMATH - a computer algebra system
    
                       UNIVERSITAET DES SAARLANDES
                         Fachbereich Mathematik
                       - Prof. Dr. H. G. Zimmer -
    
    An overview:

    	SIMATH is a computer algebra system with emphasis on algebraic
    number theory.  It was initiated as part of a cooperation between the
    Universitat des Sarrlandes and the Siemens AG.  At present SIMATH is
    running on the Siemens PCs MX2 and MX300, on the Apollo workstations
    DN3000 and DN4500 as well as on the SUN workstations 3/**.
    
    
    The Structure of SIMATH:

    	SIMATH is an open system completely written in C, but all
    SIMATH-functions can also be used in FORTRAN programs.  This is made
    possible by means of converting routines which are part of SIMATH.
    
    	The modular conception of SIMATH enables the user to include
    their own programs at every stage of the system.  SIMATH has its own
    user interface which simplifies the administration of the system and
    of the libraries.  All data types of SIMATH are realized by a list
    system organized in a dynamic manner on the basis of an automatic
    garbage collector.
    
    	For a quick and interactive attack of problems, SIMATH is
    furnished with a calculator making available most of the
    SIMATH-functions for on-line applications.  All SIMATH-functions -
    including those of the calculator - are equipped with some explanatory
    documentation and help features.  These as well as a key word index
    can be used in an interactive manner too.
    
    
    Contents:

    	SIMATH is aimed at algebraic number theory.  The following
    routines are available:
    
    -A basic arithemtic for the domains Z, Q, Z/mZ and Galois-fields
       F(q), for polynominal rings (in arbitrarily many variables) over
       these domains, and for algebraic number fields.
    
    -Chinese remainder theorem, primality testing and factorization.
    
    -Substitution, transformation, resultant, discriminant and
       factorization of polynomials.
    
    -A package of matrix and vector routines, containing:
       - a basic arithmetic of matrices and vectors over the
         above-mentioned domains.
       - modulo-calculation.
       - evaluation, substitution and Euclidean scalar product of vectors.
       - inverse, determinant, Hermite normal form, elementary divisor
         form with cofactors, characteristic polynomial and eigenvalues of
         matrices. 
       - routines for solving systems of linear equations.
    -A basic arithmetic for algebraic number fields and function fields,
       continued fraction expansions, determination of integral bases,
       prime divisor factorization, fundamental units, class numbers and
       class groups.
    -The addition of points, birational transformations, global minimal
       models and the Neron-Tate-height for elliptic curves;
    -congruence numbers.
    
    Some of the higher algorithms concerning the above topics are not
    quite finished but will be available in near future.
    
                                         Saarbrucken, February 1990

Version 3.5 of SIMATH is now available via anonymous FTP from
anonymous@ftp.math.uni-sb.de or math.uni-sb.de (134.96.32.23).


Contact:SIMATH-Gruppe
        Lehrstuhl Prof. Dr. H.G. Zimmer
        FB 9 Mathematik
        Universitaet des Saarlandes
        W-6600 Saarbrueken
	Phone: 0681/302-2206

        simath@math.uni-sb.de
