Singular

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.

email: ignfar@eis.uva.es
Posted in old Singular Forum on: 2002-02-20 11:21:46+01