xTras is a field-theory inspired add-on package for
xAct. It contains new functions for doing tensor algebra, making Ansatze, computing contractions, and much more.
Below is a list of new functionality in
xTras. If you're new to xAct, have a look at the
introduction to xAct.
MapTimed — timed version of
Map
MapTensors — map over tensors
AllContractions — gives all contractions of an expression
MakeTraceless — makes an expression traceless
ConstructDDIs — constructs dimensionally dependent identities
CollectTensors — collects all tensorial terms
CollectConstants — collects all constant symbols
SolveConstants — solves equations with respect to constant symbols
SolveTensors — solves equations with respect to tensors
Symmetrized covariant derivatives
SymmetrizeCovDs — symmetrizes covariant derivatives
ExpandSymCovDs — expands symmetric covariant derivatives
SymCovDQ — sets covariant derivatives to be symmetrizable
YoungProject — projects tensors onto a Young tableau
RiemannYoungProject — projects Riemann tensors onto their Young tableau
TableauSymmetric — generates the SGS of a Young tableau
FullSimplification — simplifies curvature tensors as much as possible
SortCovDsToDiv — automatically sorts covariant derivatives to divergences
SortCovDsToBox — automatically sorts covariant derivatives to boxes
SymRiemann — the symmetrized Riemann tensor
Schouten — the Schouten tensor
SchoutenCC — the cosmological Schouten tensor
EinsteinCC — the cosmological Einstein tensor
ToRicci — converts curvature tensors to Ricci tensors where possible
ToRiemann — converts curvature tensors to Riemann tensors where possible
KillingVectorOf — defines a Killing vector
Pseudo index-free notation
IndexFree — head for pseudo index-free expressions
ToIndexFree — converts to pseudo index-free
FromIndexFree — converts from pseudo index-free
Perturbations on (A)dS and flat backgrounds
SymmetricSpaceRules — rules for (A)dS backgrounds
ExpandBackground — perturb and expand on generic backgrounds
ExpandFlat — perturb and expand on flat backgrounds
Invariants of Riemann tensors
EulerDensity — gives the Euler density
ProductInvariants — gives a basis for invariants of Riemann tensors
ComputeBasisValues — computes values of basis elements
ImplodedTensorValues — computes values of derivatives of tensors
