Specialized computer algebra system for application in general
  relativity
Specialized computer algebra system
for application in general relativity
S.I. Tertychniy
Abstract: A brief characteristic of the specialized computer algebra
system GRGEC intended for symbolic computations in the field of
general relativity is given.
The code GRGEC constitute a full-fledged programming system intended
for application in the field of the general relativity and adjacent areas of the
differential geometry and the classical field theory. Written mostly in the lisp
dialect known as standard lisp, it is realized, structurally, as the top layer
upon the universal computer algebra system Reduce. The latter is utilized
as the primary tool for execution of the general kind symbolic mathematical
calculations. The code infrastructure includes, in particular, the user inter-
face based on the interpreter of the so called language of problem specification
which models the natural language in its simplified version adapted to the
description of the notions and relationships taking place in the application
field. The collection of algorithms implementing the set of data objects and
the rules of operations with them models the most important notions and
relationships (equations) established in the relevant areas of the physics and
the geometry. One could note in this respect implementation of the calcu-
lus of exterior forms, the spinor algebra tools, the major elements of the
tensor calculus. (All these techniques operate with separate object compo-
nents, no abstract index methods have been implemented). The application
specific algorithms enable one, in particular, to handle various bases in folia-
tions of exterior forms connected with the metric structure, the connection,
the curvature with its irreducible constituents and invariants, the equations
connecting the above objects such as Cartan equations, Bianchi equations,
various algebraic identities, the field equations of the gravity theory (Ein-
stein equations). The handling of a number of the classical field has been
implemented including electromagnetic field, massless spinor field, massive
spinor fields, massless scalar field, conformally invariant scalar field, massive
scalar field and others. It is worth noting also the feasibility to manipu-
late with Newman-Penrose spin coefficients, Lanczos representation of the
conformal curvature, Rainich theory of the coupling of electromagnetic and
gravitational fields, Killing vectors and more.
GRGEC is currently available free of charge at http://grg-ec.110mb.com
http://arxiv.org/abs/0704.1350v1
http://grg-ec.110mb.com
