  In this paper we present an algorithm to compute a Standard Basis for a
fractional ideal $\mathcal{I}$ of the local ring $\mathcal{O}$ of an $n$-space
algebroid curve with several branches. This allows us to determine the
semimodule of values of $\mathcal{I}$. When $\mathcal{I}=\mathcal{O}$, we may
obtain a (finite) set of generators of the semiring of values of the curve,
which determines its classical semigroup. In the complex context, identifying
the K\"{a}hler differential module $\Omega_{\mathcal{O}/\mathbb{C}}$ of a plane
curve with a fractional ideal of $\mathcal{O}$ and applying our algorithm, we
can compute the set of values of $\Omega_{\mathcal{O}/\mathbb{C}}$, which is an
important analytic invariant associated to the curve.
