  The ongoing progress in (nuclear) many-body theory is accompanied by an
ever-rising increase in complexity of the underlying formalisms used to solve
the stationary Schr\"odinger equation. The associated working equations at play
in state-of-the-art ab initio nuclear many-body methods can be analytically
reduced with respect to angular-momentum, i.e. $SU(2)$, quantum numbers
whenever they are effectively employed in a symmetry-restricted context. The
corresponding procedure constitutes a tedious and error-prone but yet an
integral part of the implementation of those many-body frameworks. Indeed, this
symmetry reduction is a key step to advance modern simulations to higher
accuracy since the use of symmetry-adapted tensors can decrease the
computational complexity by orders of magnitude.
  While attempts have been made in the past to automate the (anti-) commutation
rules linked to Fermionic and Bosonic algebras at play in the derivation of the
working equations, there is no systematic account to achieve the same goal for
their symmetry reduction. In this work, the first version of an automated tool
performing graph-theory-based angular-momentum reduction is presented. Taking
the symmetry-unrestricted expressions of a generic tensor network as an input,
the code provides their angular-momentum-reduced form in an error-safe way in a
matter of seconds. Several state-of-the-art many-body methods serve as examples
to demonstrate the generality of the approach and to highlight the potential
impact on the many-body community.
