摘要翻译：
考虑实二元多项式f和g，分别具有3和m个单项式项。我们证明了对于所有m>=3，在正象限上存在形式为（f,g）的系统，其根正好为2m-1。即使是M=4有7个正根的例子，在本文之前也是未知的，所以我们详细描述了这种形式的一个明确的例子。给出了具有n+4项的n-变量多项式实零集的差伦型个数的一个O(n^{11}）上界。
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英文标题：
《New Complexity Bounds for Certain Real Fewnomial Zero Sets》
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作者：
Joel Gomez, Andrew Niles, and J. Maurice Rojas
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Computer Science        计算机科学
二级分类：Computational Geometry        计算几何
分类描述：Roughly includes material in ACM Subject Classes I.3.5 and F.2.2.
大致包括ACM课程I.3.5和F.2.2中的材料。
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英文摘要：
  Consider real bivariate polynomials f and g, respectively having 3 and m monomial terms. We prove that for all m>=3, there are systems of the form (f,g) having exactly 2m-1 roots in the positive quadrant. Even examples with m=4 having 7 positive roots were unknown before this paper, so we detail an explicit example of this form. We also present an O(n^{11}) upper bound for the number of diffeotopy types of the real zero set of an n-variate polynomial with n+4 monomial terms.
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PDF链接：
https://arxiv.org/pdf/0709.2405