TensorKit$.$jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries through the ``TensorMap'' type. We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries, illustrating its practical applications through select case studies.

翻译：TensorKit.jl是一个基于Julia语言的张量计算软件包，尤其专注于具有内部对称性的张量计算。本文介绍了其设计理念、核心功能与独特特性，包括如何通过"TensorMap"类型处理阿贝尔对称性、非阿贝尔对称性以及任意子对称性。我们着重阐述了该软件的灵活性、性能表现及其扩展至新型张量类型与对称性的能力，并通过精选案例研究展示了其实际应用价值。