Assume that we have a complete intersection curve
in n dimesions, given by n-1 polynomial equations,
and a point of this curve with only one (possibly
singular) place which, after a translation, can be
assumed at the origin. Assume that we also know a
local parameter at such point, given by a rational
function on the curve.
Is there any possibility to compute with Singular
a local parametrization (up to a certain degree)
of the unique branch at that point?
If this is not possible in general, does anybody
know an alternative method to compute the order
of a rational function at such a point without
using local parametrizations?
Note: the aim is to compute the Weierstrass semigroup
of the space curve at that point, in order to construct
AG codes over towers of function fields.
Posted in old Singular Forum on: 2002-02-20 11:21:46+01