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2021-03-02
21:14:15
README.md: Add NotABug.org/reduce-algebra mirror. check-in: f2c1823149 user: trnsz@pobox.com tags: github/master, trunk
21:13:19
README.md: Enable Chisel fossil mirror links. check-in: f38b4ee496 user: trnsz@pobox.com tags: github/master, trunk
17:36:29
README.md: Comment out Chisel mirror until sync'd check-in: 6cb9f02735 user: trnsz@pobox.com tags: github/master, trunk
2021-03-01
10:35:17
multi: Update to PR autoresponder, add SECURITY.md check-in: 484f1837b4 user: jeff@gridfinity.com tags: github/master, trunk
10:35:17
multi: Update to PR autoresponder, add SECURITY.md check-in: 26b309fce8 user: jeff@gridfinity.com tags: master, trunk
04:31:58
Update .gitattributes: Exclude doc from Linguist. Closed-Leaf check-in: 7c29086699 user: jeff@gridfinity.com tags: origin/master, trunk
04:31:19
Update .gitattributes: Exclude TeX from Linguist check-in: e49b2b6cb4 user: jeff@gridfinity.com tags: origin/master, trunk

Modified .github/mergeable.yml from [f0d3389fbd] to [02c5c4d3e0]. 

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version: 2
mergeable:
  - when: pull_request.opened
    name: "Greet a contributor"
    validate: []
    pass:
      - do: comment
        payload:
          body: >
            Thanks for your contribution!  Unfortunately, we don't use GitHub pull requests to manage code contributions to this repository.  Instead, please see the [GRG Homepage](https://reduce-algebra.sourceforge.io/grg32/grg32.php), the [REDUCE Homepage](https://reduce-algebra.sourceforge.io) or the [REDUCE Support Page](https://sourceforge.net/projects/reduce-algebra/support) at Sourceforge for details on how to report a bug."
      - do: close










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version: 2
mergeable:
  - when: pull_request.opened
    name: "Greet a contributor"
    validate: []
    pass:
      - do: comment
        payload:
          body: >
            Thanks for your contribution!  Unfortunately, we don't use GitHub pull requests to manage code contributions to this repository.  Instead, please see the [GRG Homepage](https://reduce-algebra.sourceforge.io/grg32/grg32.php), the [REDUCE Homepage](https://reduce-algebra.sourceforge.io) or the [REDUCE Support Page](https://sourceforge.net/projects/reduce-algebra/support) at Sourceforge for further details."
      - do: close

Modified README.md from [10f18bcc98] to [a5e0a6df5a]. 

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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.
- 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.












## Documentation

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



## Author

```text
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](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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# **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.
- 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

- [**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
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](https://github.com/reduce-algebra/grg/blob/master/LICENSE) for full details.

----

## Homepage

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

----

Added SECURITY.md version [28b1629609]. 













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# Security Information

## Reporting a Vulnerability

As the upstream for this project seems to be currently unavailable, if any critical vulnerabilities is found, please email [\<trnsz@pobox.com\>](mailto:trnsz@pobox.com) with the details. Include "GRG3.2" in the Subject.

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