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 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/85 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-851 ER -