  The goal of the present paper is twofold. First, a novel expansion many-body
method applicable to superfluid open-shell nuclei, the so-called Bogoliubov
in-medium similarity renormalization group (BIMSRG) theory, is formulated. This
generalization of standard single-reference IMSRG theory for closed-shell
systems parallels the recent extensions of coupled cluster, self-consistent
Green's function or many-body perturbation theory. Within the realm of IMSRG
theories, BIMSRG provides an interesting alternative to the already existing
multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei.
  The algebraic equations for low-order approximations, i.e., BIMSRG(1) and
BIMSRG(2), can be derived manually without much difficulty. However, such a
methodology becomes already impractical and error prone for the derivation of
the BIMSRG(3) equations, which are eventually needed to reach high accuracy.
Based on a diagrammatic formulation of BIMSRG theory, the second objective of
the present paper is thus to describe the third version (v3.0.0) of the ADG
code that automatically (1) generates all valid BIMSRG(n) diagrams and (2)
evaluates their algebraic expressions in a matter of seconds. This is achieved
in such a way that equations can easily be retrieved for both the flow equation
and the Magnus expansion formulations of BIMSRG.
  Expanding on this work, the first future objective is to numerically
implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio
calculations of mid-mass open-shell nuclei.
