Index: README.md ================================================================== --- README.md +++ README.md @@ -1,17 +1,25 @@ # **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** graphics shells providing nice book-quality output with Greek letters, integral signs, etc. +---- + +## Features + The main built-in **GRG** capabilities are: - Connection, torsion and nonmetricity. - Curvature. - Spinorial formalism. @@ -25,14 +33,27 @@ - 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 + +- [**GRG Homepage**](https://reduce-algebra.sourceforge.io/grg32/grg32.php) +- [GitHub Mirror](https://github.com/reduce-algebra/grg/) +- [SourceHut Mirror](https://git.sr.ht/~trn/grg/) +- [Chisel Mirror](https://chiselapp.com/user/reduce-algebra/repository/grg/) + +---- ## Documentation - [User Manual and Reference Guide](https://github.com/reduce-algebra/grg/tree/master/doc) + +---- ## Author ```text Vadim V. Zhytnikov @@ -45,13 +66,19 @@ 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](https://github.com/reduce-algebra/grg/blob/master/LICENSE) for full details. -## Upstream +---- + +## Homepage - [GRG Homepage](https://reduce-algebra.sourceforge.io/grg32/grg32.php) + +----