## Files in the top-level directory from the latest check-in of branch master

- .gitattributes
- .github
- doc
- dos
- LICENSE
- README.md
- SECURITY.md
- bondi.low
- bondi.up
- compare.txt
- compile.csl
- compile.grg
- compile.psl
- expand.csl
- expand.psl
- grg.cfg
- grg.sl
- grg2tex.red
- grg32.sl
- grg32r6.txt
- grgcfg.sl
- grgclass.sl
- grgcomm.sl
- grgcomp.sl
- grgcoper.sl
- grgdecl.sl
- grggeom.sl
- grggrav.sl
- grginit.sl
- grgmacro.sl
- grgmain.sl
- grgmater.sl
- grgprin.sl
- grgproc.sl
- grgtrans.sl
- grgxcomp.sl
- grgxmacr.sl
- guide32.tex
- new-in32.txt
- pgt.low
- pgt.up
- test.red
- timing.txt
- xcompile.psl

**GRG**

## Computer Algebra System for Differential Geometry, Gravitation and Field Theory

## Introduction

The computer algebra system **GRG** is designed to make calculation in differential geometry and field theory as simple and natural as possible. **GRG** is based on the computer algebra system **REDUCE** but **GRG** has its own simple input language whose commands resemble short English phrases.

**GRG** understands tensors, spinors, vectors, differential forms and knows all standard operations with these quantities. Input form for mathematical expressions is very close to traditional mathematical notation including Einstein summation rule. **GRG** knows covariant properties of the objects: one can easily raise and lower indices, compute covariant and Lie derivatives, perform coordinate and frame transformations etc. **GRG** works in any dimension and allows one to represent tensor quantities with respect to holonomic, orthogonal and even any other arbitrary frame.

One of the key features of **GRG** is that it knows a large number of built-in usual field-theoretical and geometrical quantities and formulas for their computation providing ready solutions to many standard problems.

Another unique feature of **GRG** is that it can export results of calculations into other computer algebra system such as *Maple*, *Mathematica*, *Macsyma*, or ** REDUCE** in order to use these systems to proceed with analysis of the data. The

*LaTeX*output format is supported as well.

**GRG**is compatible with the

**REDUCE**graphical shells, providing book-quality output with Greek letters, integral signs, etc.

## Features

The main built-in **GRG** capabilities are:

- Connection, torsion and nonmetricity.
- Curvature.
- Spinorial formalism.
- Irreducible decomposition of the curvature, torsion, and nonmetricity in any dimension.
- Einstein equations.
- Scalar field with minimal and non-minimal interaction.
- Electromagnetic field.
- Yang-Mills field.
- Dirac spinor field.
- Geodesic equation.
- Null congruences and optical scalars.
- Kinematics for time-like congruences.
- Ideal and spin fluid.
- Newman-Penrose formalism.
- Gravitational equations for the theory with arbitrary gravitational Lagrangian in Riemann and Riemann-Cartan spaces.

## Availability

## Documentation

## Author

```
Vadim V. Zhytnikov
Physics Department, Faculty of Mathematics,
Moscow State Pedagogical University,
Davydovskii per. 4, Moscow 107140, Russia
Telephone (Home): (095) 188-16-11
E-mail: vvzhy@td.lpi.ac.ru
E-mail: grg@curie.phy.ncu.edu.tw
Subject: for Zhytnikov
```

## License

**GRG**is free of charge. See LICENSE for full details.