The Big Mother of all Dualities: Möller Algorithm

A General Framework for Applying FGLM Techniques to Linear Codes

“…See [3] for a more general treatment of these concepts. Note that the matphi structure is indepent of the particular set N of representative elements of the quotient K[X]/I.…”

“…In particular, it is introduced the pattern algorithm for monoid and group algebras . In [3] a more general pattern algorithm which works on modules is introduced, many things behind of this idea of using linear algebra are formalized, notions like "Gröbner technology" and "Gröbner representations" are used. There are other approches which also generalized similar ideas to some settings, behind of all these works is the essential fact of using linear algebra techniques to compute in "Gröbner bases schemes".…”

A divide-and-conquer algorithm for computing gröbner bases of syzygies in finite dimension

“…Following a path of work pioneered by Marinari, Möller and Mora [1,25,27], we focus on a specific situation where N is described using duality. That is, N is known through D linear functionals φ j : R n → K such that N = ∩ 1≤j ≤D ker(φ j ).…”

“…Namely, this assumption allows one to design iterative algorithms which compute bases of Syz N i (F ) iteratively for increasing i, until reaching i = D and obtaining the sought basis of Syz N (F ). An efficient such iterative procedure is given in [25], specifically in Algorithm 2 (variant in Section 9 therein); note that it is written for m = n = 1 and F = [1], in which case Syz N i (F ) = N i , but directly extends to the case m ≥ 1 and F ∈ R m×n .…”

The vanishing ideal of a finite set of closed points in affine space

“…First, let us take A = {(1, 0), (1,2), (3,1), (3,4)}. It is easy to write down one element of I (A):…”