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ConstructDDIs

ConstructDDIs[expr]
constructs all scalar dimensional dependent identities that can be build out of expr.
ConstructDDIs[expr, frees]
constructs all dimensional dependent identities that can be build out of expr and that have free indices frees.
ConstructDDIs[expr, frees, sym]
constructs all dimensional dependent identities that can be build out of expr and that have the symmetry sym imposed on their free indices frees.
  • ConstructDDIs returns a list of tensorial expressions that are zero due to over-antisymmetrization.
  • ConstructDDIs uses AllContractions internally, hence its conditions on the input expression also apply to ConstructDDIs.
  • The number of indices of expr plus the number of additional frees has to be at least 2 (d+1), where d is the dimension of the manifold.
  • ConstructDDIs computes all possible contractions between expr and the basic dimensional dependent identity, BasicDDI.
  • ConstructDDIs defines the BasicDDI the first time it's called.
  • ConstructDDIs only works when the dimension of the manifold is a non-generic integer.
  • It is possible to change the dimension of the manifold in between ConstructDDIs calls.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Vanishing of the Einstein tensor in 2 dimensions:
Vanishing of the Weyl tensor in 3 dimensions:
Vanishing of the Einstein tensor in 2 dimensions:
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Vanishing of the Weyl tensor in 3 dimensions:
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Possible Issues   (2)
When the dimension of the manifold is not an integer, ConstructDDIs doesn't work:
The number of indices of the input expression has to be at least 2 (d+1), where d is the dimension of the manifold.