| 摘 要： | In this paper, we study the properties of the zero set of a homotopy H: I~m×0, 1]→ and its piecewise linear approximation φ_((?)4): I~m×0, 1]→R~m, These properties are very important for the homotopy simplex pivot algorithm. However, we prove that for almost every polynomial mapping the zero set of linear homotopy H(z, t) =tp(z)+(1-t)Q(z) consists of q=multiply form j=1 to n(q_j) disjoint differential curves, and the zero set of its piecewise linear approximation φ_(δ4), consists of some broken lines. Where δ_4→0, these broken lines tend to differential curves in the zero srt of H.
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