  We provide a computer algebra package called Random Tensor Network Integrator
(RTNI). It allows to compute averages of tensor networks containing multiple
Haar-distributed random unitary matrices and deterministic symbolic tensors.
Such tensor networks are represented as multigraphs, with vertices
corresponding to tensors or random unitaries and edges corresponding to tensor
contractions. Input and output spaces of random unitaries may be subdivided
into arbitrary tensor factors, with dimensions treated symbolically. The
algorithm implements the graphical Weingarten calculus and produces a weighted
sum of tensor networks representing the average over the unitary group. We
illustrate the use of this algorithmic tool on some examples from quantum
information theory, including entropy calculations for random tensor network
states as considered in toy models for holographic duality. Mathematica and
Python implementations are supplied.
