Christoffel

• Christoffel is a reserved word in xTensor`. It is used to generate (using GiveSymbol) the name of the Christoffel tensor relating two covariant derivatives.
• Christoffel[CD][inds] is automatically converted into Christoffel[CD, PD][inds].
• Christoffel[CD1, CD2][inds] is automatically converted into GiveSymbol[Christoffel, CD1, CD2][inds] if the list {CD1, CD2} is sorted, or into -GiveSymbol[Christoffel, CD2, CD1][inds] otherwise.

• The derivatives are sorted lexicographically, except for PD which is always sorted last.
• Two derivatives CD1 and CD2 can be related by a Christoffel tensor if and only if they are compatible (this is checked using the private function CompatibleCovDsQ[CD1, CD2]), defined as follows: two derivatives are compatible iff one of them (or both) is PD and either one of them (or both) does not act on any internal vbundle or both act on the same internal vbundle.
• See: Section 4.5.
• See also: GiveSymbol.
• New in version 0.
• Last update: 17-X-2007 for version 0.9.3 of xTensor`.

Created by Mathematica  (May 16, 2008)