atlas 2 for Mathematica®

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Domain - declaration of a manifold or its domain

Domain[manifold]
Domain[]
allows one to declare different manifolds (or domains of a manifold) in one session.
  • manifold - identifier - a manifold name or a name of a manifold domain.
  • Each manifold (domain) can have its own dimension, coframe, frame, metric tensor field etc. Mapping between manifolds (domains) can be declared by the procedure Mapping. (see Mapping).
  • The Domain procedure can be used in three ways:
  • - Domain[newname] - declares a manifold (or a domain of a manifold) named newname and puts NewName as current (working) domain.
  • - Domain[oldname] - makes a manifold (or a domain of a manifold) named oldname (declared later) as current (working) domain.
  • - Domain[] - returns the name of the current domain.
  • If the user does not going to work with different manifolds in the one session then there is no need to use the Domain procedure.