SUPERCALC - a REDUCE package for commutator calculations

Seiler, Werner M.

doi:10.1016/0010-4655(91)90082-v

Cited by 9 publications

(2 citation statements)

References 11 publications

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“…In addition, there are also a number of packages (Hartmann and Davis 1989 ; Ilyin and Kryukov 1989 ; Seiler 1991 ; Jamin and Lautenbacher 1993 ; Poghosyan 2005 ; Abłamowicz and Fauser 2015 ) which provide facilities for Clifford algebras or more specifically for -matrix algebra. Such packages can be used both in quantum field theoretic and geometric calculations, but were considered too specialized to be included in Sects.…”

Section: Introductionmentioning

confidence: 99%

Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.

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Section: Introductionmentioning

confidence: 99%

Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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“…When the importance of SUSY was realized, symbolic packages were developed for problems related to it: super-Feynman diagrams [11], Lie superalgebra manipulations [12], calcula-tion of the supertrace of a supermatrix [13] and the anomaly calculation in superstring theories [14], among others. Having in mind the manipulations needed in actual SUSY and supergravity calculations, it seemed natural to develop an algorithm and implement it in one of the symbolic programming languages that could perform some of the manipulations, thereby reducing the effort one has to make in performing the calculations.…”

Section: Introductionmentioning

confidence: 99%

Dill: an algorithm and a symbolic software package for doing classical supersymmetry calculations

Lučić

1995

Computer Physics Communications

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An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica programming language. While the algorithm is quite general, the package is created for the 4 − D, N = 1 model. Nevertheless, with little modification, the package could be used for other SUSY models. The package has been tested and some of the results are presented. 1 or "human", manipulations. Therefore, Dill is intended to be used interactively; whenever a user who, while doing a complicated calculation, needs to perform one or more of the calculations defined in the package, he/she simply applies the appropriate function(s), gets a result and continues the calculation on his/her own, using Dill when needed. In order to use the package, one has to have a working knowledge of Mathematica.An application of a function returns an expression in such a format that another function can be applied on the returned expression. Unfortunately, it is not easy for a user to read such an expression, especially if it is long and has a lot of indices. In order to make it easier, a Mathematica-T E X interface was written in C. It converts the output into a T E X file using conversion rules given by the user in a separate file. The dvi file produced from the T E X file is then shown on a screen using xdvi, or, simply, saved. It is necessary to work under X-Windows and have xdvi program in order to show the file on a screen; otherwise, the dvi file can be simply processed and printed out.The main body of this article is organized as follows: Section 2 gives a simple overview of SUSY and shows the kind of calculations that can be done on a computer. Section 3 gives the algorithms for specific manipulations and Section 4 explains the way the algorithms are implemented in Mathematica software and gives information about the package for a potential user. Examples are shown in the Appendices. A Brief Introduction to Supersymmetry CalculationsThe algorithm and the package were developed for use in a SUSY calculations at the classical level. The application on a model other than 4 − D, N = 1 requires some definitions

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Mit Buchstaben auf dem Computer rechnen: Über die Anwendung der Computeralgebra in Mathematik, Naturwissenschaft und Technik

Hehl

Meyer

1992

Phys. Bl.

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Traditionellerweise rechnet man auf dem Computer mit Zahlen, d. h. numerisch. Inzwischen sind aber Software‐Pakete entwickelt worden (z. B. Axiom, Derive, Macsyma, Maple, Mathematica, Reduce), die es erlauben, mathematische Formeln auf dem Computer zu manipulieren. Man kann z. B. Polynome vereinfachen, nicht‐lineare algebraische Gleichungen analytisch lösen, Funktionen differenzieren und integrieren, Matrizen invertieren usw. Anhand einfacher Beispiele wird gezeigt, wie leistungsfähig die heutigen Systeme sind und wie man sie in Mathematik, Naturwissenschaft und Technik typischerweise anwenden kann.

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SUPERCALC - a REDUCE package for commutator calculations

Cited by 9 publications

References 11 publications

Computer algebra in gravity research

Computer algebra in gravity research

Dill: an algorithm and a symbolic software package for doing classical supersymmetry calculations

Mit Buchstaben auf dem Computer rechnen: Über die Anwendung der Computeralgebra in Mathematik, Naturwissenschaft und Technik

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