Different methods are proposed and tested for transforming a nonlinear differential system, and more particularly a hamiltonian one, into a map without having to integrate the whole orbit as in the well known Poincare map technique. We construct piecewise polynomial maps by coarse-graining the phase surface of section into parallelograms using values of the Poincare maps at the vertices to define a polynomial approximation within each cell. The numerical experiments are in good agreement with the standard map taken as a model problem. The agreement is better when the number of vertices and the order of the polynomial fit increase. The synthetic mapping obtained is not symplectic even if at vertices there is an exact interpolation. We introduce a second new method based on a global fitting. The polynomials are obtained using at once all the vertices and fitting by least square polynomes but in such a way that the symplectic character is not lost.