On the use of algebraic programming in the general relativity
This is a review devoted to some results of Algebraic Programming ( used in treating several problems of general relativity, based mainly on already published articles. The article contains the talk given by the author at The Albert Einstein Institut, Max Planck Institut fur Gravitationstheorie, Golm, Germany, september 2000

title: On the Reverse Engineering Method in Cosmologies with Non‐Minimally Coupled Scalar Field
abstract: We shall investigate the use of the so called “reverse engineering” method in reconstructing the shape of the potential in cosmologies based on a scalar field non‐minimally coupled with gravity. The main field equations (the new or modified Friedman equations) will be obtained in a cosmology with Robertson‐Walker metric. Then in a similar graphical manner as was introduced recently we shall investigate the particular case of a cosmology with exponential growth of the scale factor. This opens the route for future investigations on other examples and the general case.

title: Doing Numerical Cosmology with the Cactus Code
abstract: The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery in numerical relativity. This thorn is dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code

title: Testing The Cactus Code On Exact Solutions Of The Einstein Field Equations
abstract: The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete three-dimensional machinery for numerical relativity. We describe an application ("thorn") for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code.

title: Classical Gaussian bag in (1+1) general relativity
abstract: Relativistic geometric models generated by Gaussian conformally flat (1+1) metrics are considered. These metrics are depending on a fixed parameter and another variable parameter that play the role of coupling constant. It is shown that these models are of open bags where the relativistic massive particles remain confined for energies less than the rest one. By using numeric methods it is pointed out that inside of the bag the motion is close to an harmonic one. The dispersion function is also calculated for different values of the free parameter.

title: Gravity, torsion, Dirac field and computer algebra using MAPLE and REDUCE
abstract: The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. A comparative review of such procedures obtained for two computer algebra platforms (REDUCE + EXCALC and MAPLE + GRTensorII) is carried out. Applications for the calculus of Dirac equation on specific examples of spacetimes with or without torsion are pointed out.

title: Classical oscillators in general relativity
abstract: It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics can be used for new geometric models of closed or even open bags.