a field-theory motivated approach to computer algebra


Core general relativity package, mainly a library of various standard expressions.
Importing this library will make \partial a partial derivative and will also declare the greek indices to be space-time indices.
\partial{#}::PartialDerivative; {\mu,\nu,\rho,\sigma,\kappa,\gamma,\lambda}::Indices(spacetime, position=fixed);
\(\displaystyle{}\text{Attached property PartialDerivative to }\partial{\#}.\)
\(\displaystyle{}\text{Attached property Indices(position=fixed) to }\left[\mu, \nu, \rho, \sigma, \kappa, \gamma, \lambda\right].\)

riemann_from_christoffel(R: Ex, c: Ex) -> Ex

Generates an equality which determines the Riemann tensor in terms of the Christoffel symbols.

christoffel_from_metric(c: Ex, g: Ex) -> Ex

Generates an equality which determines the Christoffel symbols in terms of the metric.


Convert contractions of Riemann tensors to Ricci tensors or scalars.
ex:= R^{a}_{b c a} - R^{a}_{b a c};
\(\displaystyle{}R^{a}\,_{b c a}-R^{a}\,_{b a c}\)
R^{a}_{b c a}-R^{a}_{b a c}
\(\displaystyle{}-2R_{b c}\)
-2R_{b c}
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