Related papers: Computer algebra in gravity
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on…
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial…
We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in…
We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.
This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the…
On the base of the distinction between covariant and contravariant metric tensor components, an approach from algebraic geometry will be proposed, aimed at finding new solutions of the Einstein's equations both in GTCCCM and in standard…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
The Poincar\'e gauge theory of gravity has a metric compatible connection with independent dynamics that is reflected in the torsion and curvature. The theory allows two good propagating spin-0 modes. Dynamical investigations using a simple…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
We describe a method of Monte-Carlo simulations of simplicial quantum gravity coupled to matter fields. We concentrate mainly on the problem of implementing effectively the random, dynamical triangulation and building in a detailed-balance…
We present a version of the REDUCE computer algebra system as it was in the early 1970s. We show how this historical version of REDUCE may be built and run in very modest present-day environments and outline some of its capabilities.
We review the general relativistic theory of the motion, and of the timing, of binary systems containing compact objects (neutron stars or black holes). Then we indicate the various ways one can use binary pulsar data to test the…