  Many theories of gravity are spoiled by strongly coupled modes: the high
computational cost of Hamiltonian analysis can obstruct the identification of
these modes. A computer algebra implementation of the Hamiltonian constraint
algorithm for curvature and torsion theories is presented. These non-Riemannian
or Poincar\'e gauge theories suffer notoriously from strong coupling. The
implementation forms a package (the `Hamiltonian Gauge Gravity Surveyor' -
HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets
can be evaluated in parallel, meaning that Hamiltonian analysis can be done on
silicon, and at scale. Accordingly HiGGS is designed to survey the whole
Lagrangian space with high-performance computing resources (clusters and
supercomputers). To demonstrate this, the space of `outlawed' Poincar\'e gauge
theories is surveyed, in which a massive parity-even/odd vector or parity-odd
tensor torsion particle accompanies the usual graviton. The survey spans
possible configurations of teleparallel-style multiplier fields which might be
used to kill-off the strongly coupled modes, with the results to be analysed in
subsequent work. All brackets between the known primary and secondary
constraints of all theories are made available for future study. Demonstrations
are also given for using HiGGS - on a desktop computer - to run the
Dirac-Bergmann algorithm on specific theories, such as Einstein-Cartan theory
and its minimal extensions.
