I am programming in Python Hermite Interpolation, using the Lagrangian Interpolants. I have written the program to find the Lagrangian Interpolants such that I can limit the Lagrangian to a subset of the data points. My question is, when writing the Hermite Interpolation program, I need the derivatives of the Lagrangian, which I am not sure how to program for an open number subset. Is hermite interpolation by definition limited in the number of Lagrangian coefficients?