Computing a structured Gröbner basis approximately
Kosaku Nagasaka · 2011
There are several preliminary definitions for a Gröbner basis with inexact input since computing such a basis is one of the challenging problems in symbolic-numeric computations for several decades. A structured Gröbner basis is such a basis defined from the data mining point of view: how to extract a meaningful result from the given inexact input when the amount of noise is not small or we do not have enough information about the input. However, the known algorithm needs a suitable (unknown) information on terms required for a variant of the Buchberger algorithm. In this paper, we introduce an improved version of the algorithm that does not need any extra information in advance.