Abstract : We present an algorithmic way of exactly computing Belyi functions
for hypermaps and triangulations in genus $0$ or $1$, and the
associated dessins, based on a numerical iterative approach
initialized from a circle packing combined with subsequent lattice
reduction. The main advantage compared to previous methods is that
it is applicable to much larger graphs; we use very little algebraic
geometry, and aim for this paper to be as self-contained as
possible.
