We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in the Standard Model Effective Theory (SMEFT) can be obtained in a minute on a single CPU core. While our implementation focusses on SMEFT, we allow for a flexible user input of the light degrees of freedom. Furthermore, gravity, as well as additional U(1) global or gauge symmetries can be included.

中文翻译：

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..., 83106786, 114382724, 1509048322, 2343463290, 27410087742, ... 有效理论的高效希尔伯特级数

我们提出了一种用于确定有效理论的希尔伯特级数的有效算法，并在 FORM 中提供了称为 ECO（算子的有效计数）的配套代码。例如，标准模型有效理论（SMEFT）中15维算子的希尔伯特级数可以在单个CPU核上一分钟得到。虽然我们的实施侧重于 SMEFT，但我们允许灵活的用户输入轻自由度。此外，可以包括重力以及额外的 U(1) 全局或规范对称性。