Efficient Computation of Squarefree Separator Polynomials

Given a finite set of distinct points, a separator family is a set of polynomials, each one corresponding to a point of the given set, such that each of them takes value one at the corresponding point, whereas it vanishes at any other point of the set. Separator polynomials are fundamental building blocks for polynomial interpolation and they can be employed in several practical applications. Ceria and Mora recently developed a new algorithm for squarefree separator polynomials. The algorithm employs as a tool the point trie structure, first defined by Felszeghy-Ráth-Rónyai in their Lex game algorithm, which gives a compact representation of the relations among the points’ coordinates. In this paper, we propose a fast implementation in C of the aforementioned algorithm, based on an efficient storing and visiting of the point trie. We complete the implementation with tests on some sets of points, giving different configurations of the corresponding tries.