Revision history [back]

Computations of the Ricci tensor in Sage are explicit, in given coordinate charts, and you cannot keep an undefined (symbolic) metric $q_{ab}$. What you can do though is to have some components of a metric expressed in terms of (unspecified) symbolic functions. An example is provided by the Friedmann-Robertson-Walker-Lemaître metric, the components of which contain the symbolic function $a(t)$, see this notebook, which introduces as well the cosmological constant $\Lambda$ as a symbolic variable.

Regarding tensor expansions with respect to a parameter $\rho$, they are implemented in Sage, see the methods series_expansion, truncate and set_calc_order.

Computations of the Ricci tensor in Sage are explicit, in given coordinate charts, and you cannot keep an undefined (symbolic) metric $q_{ab}$. What you can do though is to have some components of a metric expressed in terms of (unspecified) symbolic functions. An example is provided by the Friedmann-Robertson-Walker-Lemaître metric, the components of which contain the symbolic function $a(t)$, see this notebook, which introduces as well the cosmological constant $\Lambda$ as a symbolic variable.

Regarding tensor expansions with respect to a parameter $\rho$, they are implemented in Sage, see the methods series_expansion, truncate and set_calc_order. and this notebook for an example of use.