Proceedings of ISP RAS

On Solving The Systems of Algebraic Equations Using Gröbner Bases.

Alexander Shokurov.


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.


Gröbner basis, ideal


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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