On Solving The Systems of Algebraic Equations Using Gröbner Bases.
Described and proved the algorithm for finding some solution of algebraic equations over arbitrary field k for zero dimension ideals if Gröbner basis of this ideal over lexicographic order is given. The found Solution lies in the algebraic closure of k. An example for a system of algebraic equations having a unique solution in the main field, and exponentially many solutions of this system is suggested.
Proceedings of the Institute for System Programming, vol. 25, 2013, pp. 195-206.
ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).
DOI: 10.15514/ISPRAS-2013-25-11Full text of the paper in pdf (in Russian) Back to the contents of the volume