Computing Puiseux Series for Algebraic Surfaces
Jan Verschelde
Abstract:
In this paper we outline an algorithmic approach to compute Puiseux
series expansions for algebraic sets.
The series expansions originate at the intersection of the algebraic set
with as many coordinate planes as the dimension of the algebraic set.
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 algebraic set.
If as many vectors in the cone as the dimension of the algebraic set 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.
This is joint work with Danko Adrovic.
The 37th International Symposium on Symoblic and Algebraic Computation
(ISSAC 2012), Grenoble, France, 22-25 July 2012.
slides of the talk