We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian tensors as well. Moreover, it can export tensor networks in the format of TensorNetwork so that one can make further calculations with concrete tensors, even for low dimensions, where the Weingarten functions differ from the ones for high dimensions. The tutorial notebooks are found at GitHub: https://github.com/MotohisaFukuda/PyRTNI2. In this paper, we explain maths behind the program and show what kind of tensor network calculations can be made with it. For the former, we interpret the element-wise moment calculus of the above random matrices and tensors in terms of tensor network diagrams, and argue that the view is natural, relating delta functions in the calculus to edges in tensor network diagrams.

翻译：我们正在升级RTNI的Python版本，该工具可对Haar分布酉矩阵上的张量网络进行符号化积分。目前，PyRTNI2已扩展支持Haar分布正交矩阵以及实/复标准高斯张量。此外，它还能以TensorNetwork格式导出张量网络，从而允许用户针对具体张量进行后续计算——即便是低维场景下（其Weingarten函数与高维情形存在差异）亦可处理。教程笔记存放于GitHub仓库：https://github.com/MotohisaFukuda/PyRTNI2。本文阐述程序背后的数学原理，并演示其可处理的张量网络计算类型。针对前者，我们以张量网络图的形式解读上述随机矩阵与张量的逐元素矩计算，论证该视角具有自然性——将计算中的δ函数与张量网络图中的边建立对应关系。