Presentations for cusped arithmetic hyperbolic lattices

We present a general method to compute presentation for any cusped arithmetic hyperbolic lattice $\Gamma$, applying classical result of Macbeath suitable $\Gamma$-invariant horoball cover the corresponding symmetric space. As applications we presentations Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ $d=1,3,7$ and quaternion PU}(2,1,\mathcal{H})$ with entries in Hurwitz integer ring $\mathcal{H}$. The implementation these is computer-assisted.