This article discusses a computational treatment of the localization
AL of an affine coordinate ring A at a prime ideal L and its
associated graded ring Gra(AL) with the means of standard basis techniques.
Building on Mora’s work, we present alternative proofs on two
of the central statements and expand on the applications mentioned by
Mora: resolutions of ideals, systems of parameters and Hilbert polynomials,
as well as dimension and regularity of AL. All algorithms are
implemented in the library graal.lib for the computer algebra system