of polynomials with numerical coefficients, its BKK-number
equals the number of its zeros, counting multiplicities. In this paper, I analyze how the knowledge of
may be used for the computation of a Gröbner basis or more generally a border basis of
. It is also shown how numerical stability may be preserved in such an approach, and how near-singular systems are recognized and handled. There remain a number of open questions which should stimulate further research.
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