Overview of Computer Algebra in Relativity

  title={Overview of Computer Algebra in Relativity},
  author={David Hartley},
Over the last few years, the use of computer algebra has become increasingly widespread in many areas of science, mathematics, and engineering. These two lectures are intended to give an idea of the range of computer algebra tools available to the relativist and the kind of problems to which they can be applied. The first lecture deals with the main general-purpose systems in use today, while the second covers systems and packages more specific to general relativity. In each case, the features… 
Computer algebra in gravity research
  • M. MacCallum
  • Computer Science
    Living reviews in relativity
  • 2018
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.
M ay 2 00 1 Computer algebra in gravity ∗
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package
Mathematics:Some Exterior Calculus
In Part A and later in Part C, we are concerned with assembling the geometric concepts that are needed to formulate a classical field theory likeelectrodynamicsand/or the theory ofgravitationin the
Symbolic Computations with Indexed Objects within
A new Mathematica package EinS is intended for calculations involving sums of indexed objects (e.g., tensors) that automatically handles implicit summations and dummy indices, and has an eecient built-in simpliication algorithm based on pattern matching.
Symbolic Computation with Indexed Objects within MATHEMATICA
The new Mathematica package EinS is intended for calculations involving sums of indexed objects (e.g., tensors) and automatically handles implicit summations and dummy indices, and has an efficient built-in simplification algorithm based on pattern matching.
Symboliccomputations with Indexed Objects within Mathematica
A newMathematica package EinS is intended for calculations involving sums of indexed objects and has an built in simpli cation algorithm based on pattern matching that handles implicit summations and dummy indices.
EinS: a Mathematica package for computations with indexed objects
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.
Independent Components of an Indexed Object with Linear Symmetries
It is proved that the number of independent components of an indexed object f(k) is a polynomial of degree not greater than the numberof indices, $k$ being the dimension of the space.


The program ORTOCARTAN for algebraic calculations in relativity
The program ORTOCARTAN can calculate the curvature tensors (Riemann, Ricci, Einstein and Weyl) from a given orthonormal tetrad representation of the metric tensor from the point of view of a user.
TTC: symbolic tensor and exterior calculus
The package TTC (Tools of Tensor Calculus) implements the majority of the basic tools of tensor and exterior calculus in a differentiable manifold using the point‐of‐view of the modern differential
CARTAN: A Mathematica package for tensor computations
CARTAN is an easy-to-use symbolic, tensor component package based on the popular Mathematica program. CARTAN makes use of the powerful formalism of rigid frames, and can return results both in this
Contributions to the study of general relativistic shear-free perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computation
It has been conjectured that general relativistic shear-free perfect uids with a barotropic equation of state, and such that the energy density, ; and the pressure, p; satisfy +p 6= 0; cannot
MathTensor - a system for doing Tensor analysis by computer
The mathtensor a system for doing tensor analysis by computer that will be your best choice for better reading book that will not spend wasted by reading this website.
Algebraic invariants of the Riemann tensor in a four‐dimensional Lorentzian space
A set of 16 scalar invariants is given of the Riemann tensor which is shown to contain complete minimal sets in the Einstein–Maxwell and perfect fluid cases. All previously known sets fail to be
The inflating wormhole: a Mathematica animation
The purpose of the current paper is to present the details of these computer simulations, and in the process introduce the reader to some techniques of simple graphing in M A T H E MA T I C A.
The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin
We find the necessary and sufficient conditions for the regularity of all scalar invariants polynomial in the Riemann tensor at the origin of spherically, cylindrically and plane symmetric static
Algebraic Simplification