The Big Mother of All the Dualities: Moeller Algorithm

M.E. Alonso, T. Mora

In 1982, Michael Moeller gave one of the first application of Groebner bases to produce Lagrange interpolation at affine points. The algorithm was in fact effectively building the whole theory of duality for 0-dimensional ideals in the polynomial ring which have today many applications to solving and has been recently generalized to the non-commutative setting. The paper is a survey on Moeller's Algorithm and its applications.