Némethi's division algorithm for zeta‐functions of plumbed 3‐manifolds

A polynomial counterpart of the Seiberg–Witten invariant associated with a negative definite plumbing 3‐manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta‐function defined by the combinatorics of the manifold. In this article we give an algorithm, based on multivariable Euclidean division of the zeta‐function, for the explicit calculation of the polynomial, in particular for the Seiberg–Witten invariant.