We present $\mathtt{bimEX}$, a Mathematica package for exact computations in 3$+$1 bimetric relativity. It is based on the $\mathtt{xAct}$ bundle, which can handle computations involving both abstract tensors and their components. In this communication, we refer to the latter case as concrete computations. The package consists of two main parts. The first part involves the abstract tensors, and focuses on how to deal with multiple metrics in $\mathtt{xAct}$. The second part takes an ansatz for the primary variables in a chart as the input, and returns the covariant BSSN bimetric equations in components in that chart. Several functions are implemented to make this process as fast and user-friendly as possible. The package has been used and tested extensively in spherical symmetry and was the workhorse in obtaining the bimetric covariant BSSN equations and reproducing the bimetric 3$+$1 equations in the spherical polar chart.

中文翻译：

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$\mathtt{bimEX}$：用于在 $3+1$ 双度量相对论中进行精确计算的 Mathematica 包

我们提出了 $\mathtt{bimEX}$，这是一个 Mathematica 包，用于在 3$+$1 双度量相对论中进行精确计算。它基于 $\mathtt{xAct}$ 包，它可以处理涉及抽象张量及其组件的计算。在本次交流中，我们将后一种情况称为具体计算。该包由两个主要部分组成。第一部分涉及抽象张量，重点讨论如何处理 $\mathtt{xAct}$ 中的多个度量。第二部分将图表中主要变量的 ansatz 作为输入，并返回该图表中组件中的协变 BSSN 双度量方程。实现了几个功能，使这个过程尽可能快速和用户友好。