  We come back to the construction of p-adic L-functions attached to cusp forms
of even weight k in the spirit of G. Stevens, R. Pollack [7] and M. Greenberg
[3] with a new unified presentation including the non-ordinary case. This
construction is based on Stevens's modular symbols rather than q-developments.
We review the proofs in order to obtain an effective algorithm guaranteeing a
given p-adic accuracy.
