Introduction and Overview

GRTensorIII is a package used for the calculation and manipulation of components of tensors and related objects. The program has been designed to operate efficiently for a wide range of applications, and allows for the use of a number of different mathematical formalisms. Algorithms are optimized for the individual formalisms, and transformations between formalisms have been made simple and intuitive. Additionally, the package allows for customization and expansion with the ability to define new objects, user-defined algorithms, and add-on libraries.

Regardless of the algorithm or formalism used, it is often the case that only certain simplifications applied at a crucial stage can make some problems tractable. For this reason, GRTensorIII has been designed to provide full control of the calculation path and of the simplifications to be performed at each stage. Once a calculation is completed, a variety of commands are available for the manipulation and simplification of results.

In designing the package, emphasis has been placed on the interface, allowing simple user input, as well as presenting readable output. Metrics and basis vectors are easily defined and can be saved for later use. Calculations are specified in an intuitive manner using a minimal number of commands.

This wiki page introduces a number of characteristics and features of the GRTensorIII computer algebra package, emphasizing its input and output facilities, the ability to define new tensor objects, and the ability to use and switch between a number of different formalisms (classical tensor methods, general bases, and null tetrads). This wiki page itself is only intended to introduce a brief overview. More detailed information regarding the commands introduced here can be found on the following wiki pages:

wiki page

• Input of Spacetimes
• Calculating Components
• Defining New Tensors
• E: Bases and tetrads (DO WE NEED A PAGE FOR THIS? OR REMOVE IT FROM THIS LIST?)
• F: Hypersurfaces, Junctions and Shells (DO WE NEED A PAGE FOR THIS? OR REMOVE IT FROM THIS LIST?)

Together these articles are intended to serve as both a user’s guide and command reference for the GRTensorIII package. Unfortunately because of this dual purpose, there are some shortfalls in their ability to perform each task: Someone looking for tutorial information might find themselves buried in uninteresting technical points, while experienced users will find some sections overly pedagogic.

It is not intended that the wiki pages be read linearly from start to finish. To begin, only the information from the first sections of the Input of Spacetimes and Calculating Components wiki pages are needed to perform some sophisticated calculations. Once familiarity with the interface is gained, the ability to define new tensors and build customized libraries, described on wiki page Defining New Tensors, greatly increase the power of the package. For the first time user, probably the best way to approach the package is to study and execute some of the demonstrations available in the worksheets directory provided with the package, referring to these wiki pages and the online help as necessary.

The version of GRTensorIII described in these wiki pages runs within the Maple environment. It has been tested with Maple 2018 in command line and worksheet mode. We encourage users to check back periodically for new versions of software, documentation, and demonstrations, at http:/github.com/grtensor/grtensor. This represents the ”official” version.

GRTensorIII software is available with documentation and examples from https://github.com/grtensor/grtensor
Source code is available from https://github.com/grtensor/grtensor3src.