Summary of some common software packages in GR
|
Package
|
Year
|
Author/publisher
|
Operating system platform(s)
|
Compatibility with OR requires:
|
General Features
|
links
|
reference
|
|
Cadabra
|
2001
|
Peeters, K.
|
Linux, MacOS (not available on Windows)
|
Standalone
|
- is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. More computational than algebraic.
|
[1]
|
[1]
|
|
Redberry
|
ca. 2013
|
Bolotin & Poslavsky
|
requires Java & Groovy
|
Standalone
|
-is similar in style to Cadabra, but provides alternative computations
|
[2]
|
[3]
|
|
Tela
|
unknown
|
unknown
|
Linux
|
Standalone
|
-is based on matrices.
|
[4]
|
[5]
|
|
Maxima
|
2008
|
Toth
|
Linux, MacOS Windows
|
|
- works with some algebraic terms, mainly results in component output
|
[6]
|
[7]
|
|
Tensor
|
unknown
|
unknown
|
|
Mathematica
|
-works mainly on components
|
|
[8]
|
|
Ricci
|
1992
|
Lee
|
|
Mathematica (2.x)
|
- is script based, but outputs algebraic expressions
|
[9]
|
[10]
|
|
TTC
|
1998
|
Balfagón & Jaén
|
unknown
|
Mathematica
|
- symbolic calculus of tensors
|
[11]
|
[12]
|
|
EDC
|
unknown
|
Bonanas
|
unknown
|
Mathematica
|
- combines symbolic algebra with processing of components; Exterior Differential Calculus
|
[13]
|
[14]
|
|
Tensorial
|
unknown
|
Cabrera
|
unknown
|
Mathematica
|
- a general tensor package
|
[15]
|
[5]
|
|
xAct
|
2002
|
José M. Martín-García
|
Windows, and probably others
|
Mathematica
|
- a suite of packages that perform a variety of algebraic and computational processes for spinors
|
[16]
|
[17] [32]
|
|
GREAT
|
unknown
|
unknown
|
unknown
|
Mathematica
|
- calculates Christoffel connections
|
|
[5]
|
|
Atlas 2
|
unknown
|
unknown
|
unknown
|
Mathematica/Maple
|
- differential geometry
|
[18]
|
[5]
|
|
GRTensor
|
unknown
|
Musgrave, Pollney & Lake
|
unknown
|
Mathematica/Maple
|
- a powerful computational package
|
[19]
|
[5]
|
|
MathGR
|
2014
|
Wang
|
unknown
|
Mathematica
|
- is both algebraic & computational
|
[20]
|
[21]
|
|
Differential Geometry
|
unknown
|
unknown
|
unknown
|
Maple
|
- a large package that applies to geometrical aspects of tensors
|
|
[5]
|
|
Riemann
|
1997
|
Portugal
|
Windows
|
Maple
|
- a package that combines some algebraic and computational functions
|
[22]
|
[23]
|
|
Canon/Invar
|
2008
|
Martin-Garcia, Yillanes & Portugal
|
Windows
|
Maple
|
- a companion program to the Riemann package, involving differential invariants
|
[24]
|
[25]
|
|
Riegeom
|
2000
|
Portugal
|
Windows
|
Maple
|
- processes index based calculations on algebraic terms
|
|
|
|
Tensor Toolbox
|
2006
|
Kolda & Bader
|
unknown
|
Matlab
|
- includes mainly computational processing
|
[27]
|
[5]
|
|
MPCA UMPCA
|
2009 2012
|
Haiping Lu
|
unknown
|
Matlab
|
Multilinear Principal Component Analysis
|
[28]
|
|
|
Physics
|
circa 2012 |
unknown
|
unknown
|
Maple | a wide-ranging tensor program, and includes many algenraic functions; mainly applies to vectors & components; does not follow traditional covariant format of some tensors and covariant differentiation |
[29]
|
|
| SHEEP | circa 1960s-1990s | d'Inverno, Cohen, Frick & Åman | DEC-20 | standalone |
calculates components of tensors for use in general relativity and general and fluid mechanics. It is associated with STENSOR for algebraic manipulation.
|
[30] | [31] |
| SHEEP2 | circa 1994 | MacCallum et al. |
Windows 10, Linux
etc associated with REDUCE |
standalone - associated with REDUCE |
SHEEP2 is a descendant of SHEEP
|
REDUCE is available
at [33] Sheep2 is available at [34] |
[1] K. Peeters, Cadabra, http://cadabra.phi-sci.com/download.html, 2001.bra.phi-sci.com/download.html, 2001..
[2] D.A. Bolotin, S.V. Poslavsky, http://redberry.cc/, 2013.
[3] D.A.P. Bolotin, S.V. Poslavsky, 'Introduction to Redberry: the computer algebra system designed for tensor manipulation, http://arxiv.org/pdf/1302.1219.pdf, 2013.
[4] http://www.linuxgoodies.com/review_tela.html
[5] http://en.wikipedia.org/wiki/Tensor_software
[6] http://maxima.sourceforge.net/
[7] Toth, V. 2005. Tensor manipulation in GPL Maxima. http://arxiv.org/abs/cs/0503073
[8] http://reference.wolfram.com/language/guide/Tensors.html
[9] http://www.math.washington.edu/~lee/Ricci/Manual.pdf
[10] http://www.math.washington.edu/~lee/Ricci/
[11] A.Balfagón, X. Jaén, TTC: Symbolic tensor calculus with indices, http://www.aip.org/cip/pdf/vol_12/iss_3/286_1.pdf, 1998.
[12] A.Balfagón ,P.Castellví and X.Jaén. Tools of Tensor Calculus, http://baldufa.upc.edu/xjaen/ttc/index.htm 2014.
[13] S. Bonanos, Capabilities of the mathematica package Riemannian geometry and tensor calculus. http://www.inp.demokritos.gr/~sbonano/RGTC/NEBX-RGTC.pdf, 2002.
[14] S. Bonanos, Riemannian Geometry & Tensor Calculus @ Mathematica, http://www.inp.demokritos.gr/~sbonano/RGTC/, 2013.
[15] http://library.wolfram.com/infocenter/Demos/434/
[16] A. G-P Gómez-Loboa, J.M. Martín-García, Spinors: A Mathematica package for doing spinor calculus in General Relativity Comp. Phys. Comm. 183 (2012) 2214-2225, arXiv: 1110.2662 [gr-qc]
[17] http://xact.es/Spinors/index.html
[18] http://www.digi-area.com/Mathematica/atlas/
[19] http://www.pma.caltech.edu/~ph236/itsinfo.html
[20] http://www.xact.es/links.html (* this link provides some other packages)
[21] Y. Wang, MathGR: a tensor and GR computation package to keep it simple, http://arxiv.org/abs/1306.1295, 2013.
[22] R. Portugal, S.L. Sautú, Applications of Maple to General Relativity, Comput. Phys. Commun., 105, (1997) 233-53.
[23] R. Portugal, The Riemann Tensor Package, http://www.cbpf.br/~portugal/Riemann.html, 2008.
[24] J.M. Martín-García, R. Portugal, L.R.U. Manssur, The Invar Tensor Package, Comput. Phys. Commun. 177 (2007) 640-648.
[25] R. Portugal, The Invar Tensor Package, http://www.lncc.br/~portugal/Invar.html, 2008.
[26] R. Portugal, The Riegeom package: abstract tensor calculation, Comput. Phys. Commun. 26 (3) (2000) 261–268.
[27] MATLAB Tensor Toolbox Version 2.5 http://www.sandia.gov/~tgkolda/TensorToolbox/index-2.5.html, 2012.
[29] http://www.maplesoft.com/products/maple/features/physics.aspx
[30] M. A. H. MacCallum and J. E. F. Skea, "SHEEP: a computer algebra system for general relativity" in "Algebraic computing in general relativity" (Proceedings of the first Brazilian school on computer algebra, vol 2)", ed. M.J. Rebou\c{c}as and W.L. Roque, Oxford University Press Oxford (1994)
[31] http://www.swmath.org/software/855
[32]
Enquiries and comments:::/p>
Enquiries and comments:::
Peter
Huf
phone +61429380524
email peterhuf@deakin.edu.au