Guessing Gröbner bases of structured ideals of relations of sequences

Assuming sufficiently many terms of an n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In applications, come along structure: for instance, may be zero outside cone, built from Gröbner basis ideal invariant under action finite group. Thus, show how to take advantage this structure reduce both number queries and operations in base recover table. applications like combinatorics, where all these make us guess fake relations, allows drastically wrong guesses. These algorithms have been implemented and, experimentally, let handle examples that could not manage otherwise. Furthermore, which kind cone lattice structures preserved by skew-polynomial multiplication. This speed up computing sparse bases group ring skew-polynomials.