We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of integer exponents, we relate our sufficient conditions to algebraic conditions that emerged in the study of toric ideals.

中文翻译：

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稀疏多项式系统至少存在一个正解的符号条件

基于度理论和盖尔对偶性，我们给出了 d 个变量中的 d 个广义多项式的稀疏系统的支持度和系数的符号条件，该系统保证至少存在一个正实根。在整数指数的情况下，我们将充分条件与复曲面理想研究中出现的代数条件联系起来。