Notes on algebra and geometry of polynomial representations
Notes on algebra and geometry of polynomial representations
复制标题
多项式表示的代数和几何注释
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Averkov
中科院分区：
文献类型：
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作者：
G. Averkov
考虑R^d中的一个半代数集合A，该集合由不等式p_i（x）>0，p_i（x）ge 0或p_i（x）=0所确定，对于给定的多项式列表p_1，.，下午。我们证明了几个符合以下模板的语句。假设在边界点的邻域内，半代数集A可以用不可约多项式f来描述。则f是某些多项式p_1，...，下午。当A是初等闭、初等开、多边形或多面体的特殊情况分别考虑。
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m. We prove several statements that fit into the following template. Assume that in a neighborhood of a boundary point the semi-algebraic set A can be described by an irreducible polynomial f. Then f is a factor of a certain multiplicity of some of the polynomials p_1,...,p_m. Special cases when A is elementary closed, elementary open, a polygon, or a polytope are considered separately.
三维多面体可以用三个多项式不等式来描述
影响因子：
0.8
作者：
Averkov
通讯作者：
Averkov