Solving Nonlinear Polynomial Systems via Symbolic-Numeric Elimination Method

@inproceedings{Zhi2004SolvingNP,
  title={Solving Nonlinear Polynomial Systems via Symbolic-Numeric Elimination Method},
  author={Lihong Zhi and Greg Reid},
  year={2004}
}
Consider a general polynomial system S in x1, . . . , xn of degree q and its corresponding vector of monomials of degree less than or equal to q. The system can be written as M0 · [xq1, xq−1 1 x2, . . . , xn, x1, . . . , xn, 1] = [0, 0, . . . , 0, 0, . . . , 0, 0] (1) in terms of its coefficient matrix M0. Here and hereafter, [...] T means the transposition. Further, [ξ1, ξ2, . . . , ξn] is one of the solutions of the polynomial system, if and only if [ξ 1 , ξ q−1 1 ξ2, . . . , ξ 2 n, ξ1… CONTINUE READING
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