Abstract
Some notes on the computation of Groebner Bases using Buchberger's algorithm over different coefficient domains and the solution of systems of algebraic equations using Groebner bases are given. Examples demonstrate applicability and its current timits, and show the wide range of problems tractable by this method. The choices of an appropriate variable ordering and a suitable term ordering are of crucial importance for the computing time and space allocation. The "optimal" variable ordering is considered, and an improvement for the selection of wdid solutions of the system of algebraic equations is described.
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