Suppose $A=\{a_1,\ldots,a_{n+2}\}\subset\mathbb{Z}^n$ has cardinality $n+2$, with all the coordinates of the $a_j$ having absolute value at most $d$, and the $a_j$ do not all lie in the same affine hyperplane. Suppose $F=(f_1,\ldots,f_n)$ is an $n\times n$ polynomial system with generic integer coefficients at most $H$ in absolute value, and $A$ the union of the sets of exponent vectors of the $f_i$. We give the first algorithm that, for any fixed $n$, counts exactly the number of real roots of $F$ in in time polynomial in $\log(dH)$.
翻译：假设$A_1,\ldots,a ⁇ n+2 ⁇ subset\mathb ⁇ n$具有最主要价值$n+2美元,所有坐标均以$a_j$的绝对值以美元为单位,而$a_j$并不全部位于同一个方形高空。假设$F=(f_1,\ldots,f_n)是按绝对值计算具有通用总计系数最高为$H的多元货币体系,而$A$则以美元为单位。我们给出的第一个算法是,对于任何固定的美元,精确计算成美元时的美元实际根数,以美元(dH)为单位。
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