Related papers: Group theory in OSCAR
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained using computations in that system. Concerning reachable…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…
The basic idea behind information algebras is that information comes in pieces, each referring to a certain question, that these pieces can be combined or aggregated and that the part relating to a given question can be extracted. This…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categories of black boxes and their morphisms. This makes new…
An Eggert-operad is a variant of Mac Lane's notion of a PROP, for which not only bijective maps, but all maps between standard finite sets, are part of the structure. We construct the free Eggert-operad and prove the universal property it…
Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…
A heap is a structure with a ternary operation which is intuitively a group with forgotten unit element. Quantum heaps are associative algebras with a ternary cooperation which are to the Hopf algebras what heaps are to groups, and, in…
In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids; and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many…