On the number of cells defined by a family of polynomials on a variety
On the number of cells defined by a family of polynomials on a variety
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关于由一系列多项式定义的细胞数量
DOI：
10.1112/s0025579300011621
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发表时间：
1996
期刊：
影响因子：
0.8
通讯作者：
Marie
中科院分区：
文献类型：
--
作者：
S. Basu;Richard Pollak;Marie
让R为真实的闭合场，多种真实尺寸K'，它是最多d的多项式q∈R[x 1，…，x k]的零集。 1，…，p s}⊂r [x 1，…，x k]，其中每个多项式最多都具有d，我们证明由Over定义的单元格数为（o（d））k请注意结合的组合部分取决于品种的维度而不是在环境空间的尺寸上。
Let R be a real closed field and a variety of real dimension k ′ which is the zero set of a polynomial Q ∈ R [ X 1 ,…, X k ] of degree at most d . Given a family of s polynomials = { P 1 ,…, P s }⊂ R [ X 1 ,…, X k ] where each polynomial in has degree at most d , we prove that the number of cells defined by over is ( O ( d )) k Note that the combinatorial part of the bound depends on the dimension of the variety rather than on the dimension of the ambient space.