Related papers: Matroids: A Macaulay2 package
We describe the computation of a catalogue containing all matroids with up to nine elements, and present some fundamental data arising from this cataogue. Our computation confirms and extends the results obtained in the 1960s by Blackburn,…
An affine variety induces the structure of an algebraic matroid on the set of coordinates of the ambient space. The matroid has two natural decorations: a circuit polynomial attached to each circuit, and the degree of the projection map to…
Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a…
We study paving matroids, their realization spaces, and their closures, along with matroid varieties and circuit varieties. Within this context, we introduce three distinct methods for generating polynomials within the associated ideals of…
In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta.…
We present a Macaulay2 package that produces compactifications of adjoint orbits and of the fibres of symplectic Lefschetz fibrations on them. We use Macaulay2 functions to calculate the corresponding Hodge diamonds, which then reveal…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
Finite group actions on free resolutions and modules arise naturally in many interesting examples. Understanding these actions amounts to describing the terms of a free resolution or the graded components of a module as group…
We describe Maple packages for the automatic generation of generating functions(and series expansions) for counting lattice animals(fixed polyominoes), in the two-dimensional hexagonal lattice, of bounded but arbitrary width. Our Maple…
In this work we announce the Maple package conley to compute connection and C-connection matrices. conley is based on our abstract homological algebra package homalg. We emphasize that the notion of braids is irrelevant for the definition…
Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different…
This paper presents a Matlab toolbox to perform basic image processing and visualization tasks, particularly designed for medical image processing. The functionalities available are similar to basic functions found in other non-Matlab…
This is a companion piece to my paper on "Example-Based Procedural Modeling Using Graph Grammars." This paper examines some of the theoretical issues in more detail. This paper discusses some more complex parts of the implementation, why…
We present pyroomacoustics, a software package aimed at the rapid development and testing of audio array processing algorithms. The content of the package can be divided into three main components: an intuitive Python object-oriented…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
Treating a realistic problem in any field of reaction kinetics raises a series of problems: we review these illustrated with examples using ReactionKinetics, a Mathematica based package.
The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path coordinates. This series almost uniquely characterizes the path up to translation and reparameterization.…