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(* :Title: xTerior *)

(* :Author: Alfonso Garcia-Parrado Gomez-Lobo and Leo C. Stein *)

(* :Summary: exterior calculus in Differential Geometry *)

(* :Brief Discussion:
   - xTerior extends xAct to work with differentiable forms in general \
manifolds.
   - Introduces the exterior algebra, the exterior derivative, the Hodge \
dual, the connection and curvature forms for an arbitrary connection, the \
exterior covariant derivative.
   
*)
  
(* :Context: xAct`xTerior` *)

(* :Package Version: 0.9.1 *)

(* :Copyright: Alfonso Garcia-Parrado Gomez-Lobo and Leo C. Stein (2013-2019) \
*)

(* :History: See xTerior.History *)

(* :Keywords: *)

(* :Source: xTerior.nb *)

(* :Warning: *)

(* :Mathematica Version: 9.0 and later *)

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IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY \
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LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED \
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The wedge product is an associative, anticommutative (actually \
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The wedge product is eliminated when found with only one argument:\
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In this section we implement the Wedge product of CTensor objects. This code \
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Wedge product of frame and co-frame with CTensor objects. We first have a \
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In this section we implement the CircleTimes product of CTensor objects. This \
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There are two objects we need for covariant exterior derivatives. First, \
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From a mathematical point of view the connection form should not be regarded \
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Lie and diff commute (probably not true for covariant exterior derivatives). \
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Lie derivative of a tensor valued differential form. We overload the xTensor \
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derivations, in whatever order you want. The sign is + just for [odd,odd] so \
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1. requires no action (it will just be automatically killed).
2, 3. Maybe have this sorted automatically? Any canonical order for v,w \
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4, 5, 6\[LongDash]write rules to go in either direction.\
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adjoint to the exterior derivative, the codifferential, requires a Hodge \
dual, which we define via a (non-degenerate!) metric. Therefore FormVarD has \
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