Related papers: The free group in R
In this short article I introduce the frab package which provides an alternative interpretation of named vectors in the R programming language; it is available on CRAN. The underlying mathematical object is the free Abelian group.
The free algebra is an interesting and useful algebraic object. Here I introduce "freealg", an R package which furnishes computational support for free algebras. The package uses the standard template library's "map" class for efficiency,…
Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.
Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example,…
This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests and decomposable models minimizing information criteria such as AIC or…
R packages are the fundamental units of reproducible code in R, providing a mechanism for distributing user-developed code, documentation, and data. Docker is a virtualization technology that allows applications and their dependencies to be…
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm…
In this short article I introduce the mvp package, which provides some functionality for handling multivariate polynomials. The package uses the C++ Standard Template Library's map class to store and retrieve elements; it conforms to…
In this short article I introduce the spray package, which provides some functionality for handling sparse arrays. The package uses the C++ Standard Template Library's map class to store and retrieve elements. One natural application for…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
In this short article I introduce the knotR package, which creates two dimensional knot diagrams optimized for visual appearance using the R programming language. The knotR package is a systematic R-centric suite of software for the…
In this short article I introduce the evitaicossa package which provides functionality for antiassociative algebras in the R programming language; it is available on CRAN at https://CRAN.R-project.org/package=evitaicossa.
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…
Let V(KG) be the normalized group of units of the group ring KG of a non-Dedekind group G with nontrivial torsion part t(G) over the integral domain K. We give a simple method for constructing free objects in V(KG).In particular, we show…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…
A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…
This paper provides a description of the algorithms employed by the Warwick AUTOMATA package for calculating the finite state automata associated with a short-lex automatic group. The aim is to provide an overview of the whole process,…
We present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group $G$, compute a finite graph of groups $\mathcal{G}$ with finite vertex groups and fundamental group $G$. Our…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…