Overview of Computer Algebra in Relativity

@inproceedings{Hartley1996OverviewOC,
  title={Overview of Computer Algebra in Relativity},
  author={David Hartley},
  year={1996}
}
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… 
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References

SHOWING 1-9 OF 9 REFERENCES
The program ORTOCARTAN for algebraic calculations in relativity
TLDR
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
TLDR
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
TLDR
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