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.

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## Features

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

## 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/)
- [NotABug Mirror](https://notabug.org/reduce-algebra/grg)
- [Chisel Mirrpr](https://chiselapp.com/user/reduce-algebra/repository/grg)

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## Documentation

- [User Manual and Reference Guide](https://github.com/reduce-algebra/grg/tree/master/doc)