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grg: Computer Algebra System for Differential Geometry, Gravitation and Field Theory, automatically mirrored from https://reduce-algebra.sourceforge.io/grg32/grg32.php https://reduce-algebra.sourceforge.io/grg32/grg32.php

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DeepSource Bot 366704470c Update .deepsource.toml 3 år sedan
.github abf1973925 multi: Update to PR autoresponder, add SECURITY.md 3 år sedan
doc 4f56cf5667 Create `doc` subdirectory, organize documentation. 3 år sedan
dos f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
.deepsource.toml 18e5dd325a Add .deepsource.toml 3 år sedan
.gitattributes 9365be23d0 Update .gitattributes: Exclude doc from Linguist. 3 år sedan
LICENSE f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
README.md 2845056cb5 Update README.md: Add link to GitLab mirror. 3 år sedan
SECURITY.md abf1973925 multi: Update to PR autoresponder, add SECURITY.md 3 år sedan
bondi.low f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
bondi.up f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
compare.txt f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
compile.csl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
compile.grg f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
compile.psl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
expand.csl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
expand.psl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grg.cfg f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grg.sl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grg2tex.red f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grg32.sl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grg32r6.txt f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
grgcfg.sl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
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guide32.tex f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
new-in32.txt f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
pgt.low f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
pgt.up f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
test.red f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan
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xcompile.psl f8c7dc117c Initial checkin: GRG 3.2 Release 6 (July 16, 2000) 3 år sedan

README.md

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.

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