Related papers: A Macaulay 2 interface for Normaliz
Many existing translation averaging algorithms are either sensitive to disparate camera baselines and have to rely on extensive preprocessing to improve the observed Epipolar Geometry graph, or if they are robust against disparate camera…
Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model…
In this article we describe mathematically relevant extensions to Normaliz that were added to it during the support by the DFG SPP "Algorithmische und Experimentelle Methoden in Algebra, Geometrie und Zahlentheorie": nonpointed cones,…
Using discrete Morse theory, Batzies and Welker introduced Morse resolutions of monomial ideals. In this note, we present the {\it Macaulay2} package {\tt MorseResolutions} for working with two important classes of Morse resolutions:…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
The Collatz process is defined on natural numbers by iterating the map $T(x) = T_0(x) = x/2$ when $x\in\mathbb{N}$ is even and $T(x)=T_1(x) =(3x+1)/2$ when $x$ is odd. In an effort to understand its dynamics, and since Generalised Collatz…
In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation for a Leibniz algebra in order to realize the abstract…
The normalizing layer has become one of the basic configurations of deep learning models, but it still suffers from computational inefficiency, interpretability difficulties, and low generality. After gaining a deeper understanding of the…
We initiate a study of Hilbert modules over the polynomial algebra A=C[z_1,...,z_d] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity…
We introduce the $\textit{Macaulay2}$ package $\texttt{OIGroebnerBases}$ for working with OI-modules over Noetherian polynomial OI-algebras. The main methods implement OI-analogues of Buchberger's algorithm and Schreyer's theorem to compute…
We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing…
The Koszul homology of modules of the polynomial ring $R$ is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we…
We introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes.
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
The package Binomials contains implementations of specialized algorithms for binomial ideals, including primary decomposition into binomial ideals. The current implementation works in characteristic zero. Primary decomposition is restricted…
The normalized eight-point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization has greatly improved the performance of the direct linear transformation algorithm. A…
Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exponential or greater. In this setting, experimentation is…
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each…
We give a description of a new Macaulay2 package called SimplicialPosets. This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals. For practical purposes, we also introduce…
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…