|We introduce an algorithm to compute Groebner
bases within linear algebra. For a given finite set of polynomials, it
compute both an appropriate term ordering and the corresponding reduced
Groenber basis of the ideal generated by the given polynomials.
Though our original algorithm changes term orderings dynamically for
computational efficiency, it is also possible to change them suitable
for the Suzuki-Sato algorithm, which compute comprehensive Groebner
basis. In this talk, we argue on the algorithms and its implementations.