xTras package
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.
Basic functions
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
Tensor algebra
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
Young tableaux
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
Curvature tensors
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
Killing vectors
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
xCoba extensions
ComputeBasisValues computes values of basis elements
ImplodedTensorValues computes values of derivatives of tensors