Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts (weighted) lattice points in polytopes. We deduce an effective algorithm in order to compute the Ehrhart polynomial of a simplex containing the origin as an interior point.

中文翻译：

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多项式的Ehrhart多项式和Laurent多项式的无穷大

从奇异性理论，几何学和组合学获得了不同的结果，我们表明，驯服的Laurent多项式在无穷远处的光谱计数了多表位中的（加权）晶格点。我们推导了一种有效的算法，以计算包含原点作为内部点的单纯形的Ehrhart多项式。