摘要翻译：
利用多项式完全交集的Gale对偶，并利用正解的fewnomial界的证明，得到了具有n+k+1个单项式的n个变量的n个多项式系统的非零实解个数的界(E^4+3)2^(k选择2)n^k/4,其指数向量生成奇数指数的Z^n子群。该界仅以常数因子(E^4+3)/(E^2+3)超过正解的界，并且对于k固定和n大的情况，该界是渐近尖锐的。
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英文标题：
《Bounds on the number of real solutions to polynomial equations》
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作者：
Daniel J. Bates (IMA), Fr\'ed\'eric Bihan (Universit\'e de Savoie),
  and Frank Sottile (Texas A&M)
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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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英文摘要：
  We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the number of non-zero real solutions to a system of n polynomials in n variables having n+k+1 monomials whose exponent vectors generate a subgroup of Z^n of odd index. This bound exceeds the bound for positive solutions only by the constant factor (e^4+3)/(e^2+3) and it is asymptotically sharp for k fixed and n large.
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PDF链接：
https://arxiv.org/pdf/0706.4134