Given a set $\mathcal A = \{a_1,\ldots,a_n\} \subset \mathbb{N}^m$ of nonzerovectors defining a simplicial toric ideal $I_{\mathcal A} \subsetk[x_1,...,x_n]$, where $k$ is an arbitrary field, we provide an algorithm forchecking whether $I_{\mathcal A}$ is a complete intersection. This algorithmdoes not require the explicit computation of a minimal set of generators of$I_{\mathcal A}$. The algorithm is based on the application of some new resultsconcerning toric ideals to the simplicial case. For homogenous simplicial toricideals, we provide a simpler version of this algorithm. Moreover, when $k$ isan algebraically closed field, we list all ideal-theoretic completeintersection simplicial projective toric varieties that are either smooth orhave one singular point.
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机译：给定$ \ mathcal A = \ {a_1，\ ldots，a_n \} \ subset \ mathbb {N} ^ m $非零向量定义了简单复曲面理想$ I _ {\ mathcal A} \ subsetk [x_1，... ，x_n] $，其中$ k $是一个任意字段，我们提供一种算法来检查$ I _ {\ mathcal A} $是否是一个完整的交集。此算法不需要显式计算$ I _ {\ mathcal A} $的最小生成器集。该算法基于将复曲面理想化的一些新结果应用于简单情况。对于同质简单杀人罪，我们提供了该算法的简单版本。此外，当$ k $是一个代数封闭域时，我们列出所有理想理论完全相交的简单投影投射复曲面变体，这些变体是光滑的或具有一个奇异点。
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