In recent years, plane curves and holomorphic differentials have proven to have a critical impact in mathematical physics, including quantum field theory, mirror symmetry or string theory. These functions implement very classical constructions found in literature and most (possibly all) already existing in SAGE, Magma, etc.
This was originally designed to study the highly singular character varieties arising from knot theory, more specifically the A-polynomial. However, there is nothing specific about these varieties, and these functions can be used in much more generality.
See this Mathematica notebook