Proposal for the Algorithmic Use of the BKK-Number in the Algebraic Reduction of a O-dimensional Polynomial System
Hans J. Stetter · Birkhäuser Basel eBooks · 2007
For a regular 0-dimensional system P of polynomials with numerical coefficients, its BKK-number m equals the number of its zeros, counting multiplicities. In this paper, I analyze how the knowledge of m may be used for the computation of a Gröbner basis or more generally a border basis of P. 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.