Computing Puiseux Series for Algebraic Surfaces
Danko Adrovic and
Jan Verschelde
Abstract:
In this paper we outline an algorithmic approach to compute Puiseux
series expansions for algebraic surfaces.
The series expansions originate at the intersection of the surface
with as many coordinate planes as the dimension of the surface.
Our approach starts with a polyhedral method to compute cones of normal
vectors to the Newton polytopes of the given polynomial system
that defines the surface.
If as many vectors in the cone as the dimension of the surface define an
initial form system that has isolated solutions, then those vectors are
potential tropisms for the initial term of the Puiseux series expansion.
Our preliminary methods produce exact representations for solution sets
of the cyclic n-roots problem, for n = m^2, corresponding to a result
of Backelin