  In this paper, we propose a feasible algorithm to give an explicit basis of
the space of regular differential forms on the nonsingular projective model of
any given plane algebraic curve. The algorithm is demonstrated for concrete
examples, with our implementation over the computer algebra system Magma. As an
application, we also describe the Cartier-Manin matrix of the nonsingular
projective curve with respect to the basis computed by the algorithm.

Algebraic Geometry;Number Theory