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2021-03-01
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Modified README.md from [b55da4bd58] to [77ad06558f].

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# GRG

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

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.

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.
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# **GRG**

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

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.

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.
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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

- [GRG Homepage](https://reduce-algebra.sourceforge.io/grg32/grg32.php)







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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

- [GRG Homepage](https://reduce-algebra.sourceforge.io/grg32/grg32.php)


GRG for REDUCE
GRG Homepage | GitHub Mirror | SourceHut Mirror | NotABug Mirror | Chisel Mirror | Chisel RSS ]