关于实多元多项式的符号条件
On sign conditions over real multivariate polynomials
摘要：
我们提出了一个新的概率算法，以找到一个有限集的点相交的每个连通组件的实现的每个符号条件的封闭在一个家庭的实多项式定义的正则超曲面，横向相交。这使我们能够显示一个概率过程，列出所有可行的符号条件的多项式。此外，我们将这些结果推广到任意实多元多项式族上闭符号条件的情形。这些程序的复杂性界限，提高了已知的。
英文摘要：
We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that intersect transversally. This enables us to show a probabilistic procedure to list all feasible sign conditions over the polynomials. In addition, we extend these results to the case of closed sign conditions over an arbitrary family of real multivariate polynomials. The complexity bounds for these procedures improve the known ones.
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