Abstract
Computing a Grobner basis for the given polynomial system with inexact (erroneous) coefficients is one of the challenging problems in symbolic-numeric computations and there are several approaches to find an approximate Grobner basis that are usually computed by floating-point numbers. However, in general the resulting basis is not a Grobner basis and does not generate the given ideal. This is the problem of all kinds of approximate Grobner bases even though there are some workarounds (with concepts of approximate basis, ideal and so on). In this paper, we introduce a proof of concept method and open questions to find an exact result from those approximate Grobner bases, that is a Grobner basis of the ideal generated by a nearby polynomial set in the exact sense.
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