Related papers: Linear groups and computation
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
This is an exercise based approach to matrix groups. The idea is to collect a bunch of exercises at one place which anyone with basic knowledge of linear algebra can attempt to solve and learn matrix groups and algebraic groups.
We survey new results on finite groups of birational transformations of algebraic varieties.
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…