The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classificati... more The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classification of the Ricci tensor of spacetimes in general relativity both depend on multiplicities of the roots of quartic equations. The coefficients in these quartic equations may be complicated functions of the space-time coordinates. We review briefly the general theory of quartic equations and then consider practical algorithms for determination of the multiplicities of their roots and hence for the classification of Riemann tensors. Preliminary results of tests of computer implementations of these algorithms, using the computer algebra system SHEEP, are reported.
ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinat... more ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinate choice and is the problem of deciding whether two apparently, different space-times are (locally) identical or not. Here we review the basic procedure for resolving this question, and its practical implementation, as presented in previous papers, and report on recent theoretical and practical research in this area. Some of the techniques are of interest in other problems; in particular, they may be applicable to tests of the equivalence of systems of differential equations.
ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinat... more ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinate choice and is the problem of deciding whether two apparently, different space-times are (locally) identical or not. Here we review the basic procedure for resolving this question, and its practical implementation, as presented in previous papers, and report on recent theoretical and practical research in this area. Some of the techniques are of interest in other problems; in particular, they may be applicable to tests of the equivalence of systems of differential equations.
The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classificati... more The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classification of the Ricci tensor of spacetimes in general relativity both depend on multiplicities of the roots of quartic equations. The coefficients in these quartic equations may be complicated functions of the space-time coordinates. We review briefly the general theory of quartic equations and then consider practical algorithms for determination of the multiplicities of their roots and hence for the classification of Riemann tensors. Preliminary results of tests of computer implementations of these algorithms, using the computer algebra system SHEEP, are reported.
This paper shows how the user can manipulate the process of searching for known (method) function... more This paper shows how the user can manipulate the process of searching for known (method) functions and at the same time provide their own tagging mechanism through a single interface.
The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classificati... more The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classification of the Ricci tensor of spacetimes in general relativity both depend on multiplicities of the roots of quartic equations. The coefficients in these quartic equations may be complicated functions of the space-time coordinates. We review briefly the general theory of quartic equations and then consider practical algorithms for determination of the multiplicities of their roots and hence for the classification of Riemann tensors. Preliminary results of tests of computer implementations of these algorithms, using the computer algebra system SHEEP, are reported.
ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinat... more ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinate choice and is the problem of deciding whether two apparently, different space-times are (locally) identical or not. Here we review the basic procedure for resolving this question, and its practical implementation, as presented in previous papers, and report on recent theoretical and practical research in this area. Some of the techniques are of interest in other problems; in particular, they may be applicable to tests of the equivalence of systems of differential equations.
ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinat... more ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinate choice and is the problem of deciding whether two apparently, different space-times are (locally) identical or not. Here we review the basic procedure for resolving this question, and its practical implementation, as presented in previous papers, and report on recent theoretical and practical research in this area. Some of the techniques are of interest in other problems; in particular, they may be applicable to tests of the equivalence of systems of differential equations.
The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classificati... more The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classification of the Ricci tensor of spacetimes in general relativity both depend on multiplicities of the roots of quartic equations. The coefficients in these quartic equations may be complicated functions of the space-time coordinates. We review briefly the general theory of quartic equations and then consider practical algorithms for determination of the multiplicities of their roots and hence for the classification of Riemann tensors. Preliminary results of tests of computer implementations of these algorithms, using the computer algebra system SHEEP, are reported.
This paper shows how the user can manipulate the process of searching for known (method) function... more This paper shows how the user can manipulate the process of searching for known (method) functions and at the same time provide their own tagging mechanism through a single interface.
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Papers by Gordon Joly