Related papers: Calculating Subgroups with GAP
This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number…
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
In earlier work, the first author outlined an algorithm for calculating a parametrization of the conjugacy classes in a Sylow $p$-subgroup $U(q)$ of a finite Chevalley group $G(q)$, valid when $q$ is a power of a good prime for $G(q)$. In…
Previously the second author has constructed by cobordism methods, an invariant associated to a finite group $G$. This invariant approximates the number of subgroups of a group, giving in some cases the number of abelian and cyclic…
We review some aspects of the use of a technique known as group averaging, which provides a tool for the study of constrained systems. We focus our attention on the case where the gauge group is non-compact, and a `renormalized' group…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
This is the report of a project with the aim to make a new implementation of the Schreier-Sims algorithm in GAP, specialized for matrix groups. The standard Schreier-Sims algorithm is described in some detail, followed by descriptions of…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
Let $F$ be a finitely generated free group. We present an algorithm such that, given a subgroup $H\leqslant F$, decides whether $H$ is the fixed subgroup of some family of automorphisms, or family of endomorphisms of $F$ and, in the…
The classification of finite groups under monoidal equivalence is a fundamental topic in the study of finite quantum groups. While a complete classification has been established for all groups of order strictly less than 64, the case for…
In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing…
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…
Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ the…