TY - GEN A1 - Möller, H. Michael T1 - On decomposing systems of polynomial equations with finitely many solutions. N2 - This paper deals with systems of $m$ polynomial equations in $n$ unknown, which have only finitely many solutions. A method is presented which decomposes the solution set into finitely many subsets, each of them given by a system of type \begin{displaymath} f_1(x_1)=0, f_2(x_1,x_2)=0,...,f_n(x_1,...,x_n)=0. \end{displaymath} The main tools for the decomposition are from ideal theory and use symbolical manipulations. For the ideal generated by the polynomials which describe the solution set, a lexicographical Gröbner basis is required. A particular element of this basis allows the decomposition of the solution set. A recursive application of these decomposition techniques gives finally the triangular subsystems. The algorithm gives even for non-finite solution sets often also usable decompositions. {\bf Keywords:} Algebraic variety decomposition, Gröbner bases, systems of nonlinear equations. T3 - ZIB-Report - SC-92-15 KW - Algebraic variety decomposition KW - Groebner bases KW - systems of nonlinear equations Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-851 ER - TY - GEN A1 - Melenk, Herbert A1 - Möller, H. Michael A1 - Neun, Winfried T1 - Symbolic Solution of Large Stationary Chemical Kinetics Problems. N2 - The paper presents a new application of computer algebra to the treatment of steady states of reaction systems. The method is based on the Buchberger algorithm. This algorithm was modified such that it can exploit the special structure of the equations derived from reaction systems, so even large systems can be handled. In contrast to numerical approximation techniques, the algebraic solution gives a complete and definite overview of the solution space and it is even applicable when parameter values are unknown or undetermined. The algorithm, its adaptation to the problem class and its application to selected examples are presented. T3 - ZIB-Report - SC-88-07 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-157 ER - TY - GEN A1 - Möller, H. Michael T1 - Multivariate Rational Interpolation: Reconstruction of Rational Functions. N2 - In this paper we consider the problem of reconstructing a multivariate rational function, when only its values at sufficiently many points are known. We use for the reconstruction of bivariate rational functions a bivariate rational interpolation operator investigated by Siemaszko [7] and a new one, compare both by examples in a Computer Algebra system, and present their multivariate generalizations. {\bf Keywords:} Multivariate rational interpolation, reconstruction, symbolic computation. T3 - ZIB-Report - SC-89-04 KW - Multivariante rational interpolation KW - reconstruction KW - symbolic computation Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-227 ER - TY - GEN A1 - Melenk, Herbert A1 - Möller, H. Michael A1 - Neun, Winfried T1 - On Gröbner Bases Computation on a Supercomputer Using REDUCE. N2 - Gröbner bases are the main tool for solving systems of algebraic equations and some other problems in connection with polynomial ideals using Computer Algebra Systems. The procedure for the computation of Gröbner bases in REDUCE 3.3 has been modified in order to solve more complicated algebraic systems of equations by some general improvements and by some tools based on the specific resources of the CRAY X-MP. We present this modification and illustrate it by examples. T3 - ZIB-Report - SC-88-02 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-107 ER -