Proceedings of ISP RAS


On Solving The Systems of Algebraic Equations Using Gröbner Bases.

Alexander Shokurov.

Abstract

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.

Keywords

Gröbner basis, ideal

Edition

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-2013-25-11

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