A general algorithm is derived for solving the congruence a≡bg mod xn for a range of term orders defined by the conditions on the particular solution required, inspired by the key equation for alternant codes.Expand

Abstract We construct a degree theory for oriented Fredholm mappings of index zero between open subsets of Banach spaces and between Banach manifolds. Our approach is based on the orientation of… Expand

We develop an integer valued degree theory for quasilinear Fredholm maps. This class of maps is large enough so we can place in this framework all fully nonlinear elliptic boundary value problems… Expand

In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gröbner basis of this ideal with respect to a total degree ordering. In the first… Expand

Assuming that X and Y are Banach spaces and a:(a, b) —» ?2?(X, Y) is a path of linear Fredholm operators with invertible endpoints, in (F-Pl) we defined a homotopy invariant of a, a(a, I) G Z2 , the… Expand