On Solving The Systems of Algebraic Equations Using Gröbner Bases
Alexander Vladimirovich Shokurov · Proceedings of the Institute for System Programming of RAS · 2013
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.