An extension of buchberger's algorithm to compute all reduced gröbner bases of a polynomial ideal
In this paper we present for the bivariate case an algorithm to compute all possible reduced Gröbner bases of a polynomial ideal. This algorithm is an extension of Buchberger's one, which is based on the possibility to classify and to handle easy all term orderings in case of two variables. The constructed algorithm is interesting for the study of complexity of constructing Gröbner bases in dependence of the chosen term ordering and may lead to new insights on the question which is the best term ordering for quick termination.
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