  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.
