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2013
Moved code from the notebook xTeriorAlgebra.nb to the notebook
xTerior.nb which contains the code of the package. The following
are the main differences between the code which was written in
the notebook xTeriorAlgebra.nb and what has been put in the notebook
xTerior.nb
-The notation for the exterior derivative is ExtDiff[form]. ExtDiff should
be independent from any covariant derivative, as the exterior derivative
only requires the differential structure for its definition.
-The notation for the exterior covariant derivative is
ExtCovDiff[form,covd]. ExtCovDiff[expr] is automatically transformed into
ExtCovDiff[expr,PD]
-Connection forms: The notation for the connection 1-form is
ConnectionForm[CovD,VBundle][a,-b]. The connection isn't regarded as the
difference between two connections as it represents a connection in
a principal bundle. If VBundle=TangentBundle then one has the automatic
transformation
ConnectionForm[covd,TangentBundle]->ChristoffelForm[covd]
In addition we set ConnectionForm[PD,VBundle]=0, ChristoffelForm[PD]=0.
The user cannot change the index layout of the connection forms
-Curvature forms: The notation for the curvature 2-form is
CurvatureForm[covd,VBundle][a,-b]. If VBundle=TangentBundle then we
have the automatic rule
CurvatureForm[covd,TangentBundle][a,-b]=RiemannForm[covd][a,-b].
The index layout cannot be changed by the user.
-Added the command ExpandExtDiff whose syntax is ExpandExtDiff[expr,covd]
This command handles the Cartan eqs. and the expansion of the exterior
derivative in a coordinate chart.
-The notation for the co-differential is CoDiff. The codifferential has been
made independent from any covariant derivative because we don't need a
covariant derivative to define the co-differential. This affects the
last lines of the code of FormVarD.
6 Nov. 2013: added automatic contraction of basis elements in their product with
the exterior derivative.
10 Nov. 2013: added ConnectionFormToTensor and CurvatureFormToTensor.
1 Dec. 2013: -added ?CovDQ in the definition of ConnectionForm and ChristoffelForm
as non-atomic tensors (section 3.1).
-Changed the on-line help of Connection form and ChristoffelForm to adapt them to
their new syntax.
-Added the covariant derivative to the list of HostsOf ConnectionForm, ChristoffelForm,
RiemannForm, CurvatureForm.
10 Dec. 2013: -added the condition that the exterior derivative of Basis objects is zero.
Suppressed addition of 6th Nov.
11 Dec. 2013: -Enlarged the code of ExpandHodgeDual to admit exterior powers
of coordinates.
12 Dec. 2013: Fixed bug in ExpandExtDiff.
18 Dec. 2013: Suppressed $DefInfoQ in section 1.4. Added DefInfo->Null in a number of Def commands.
Deg is now an argument of DefDifferentialForm and not an option.
22 Dec. 2013: Suppressed symbol ExtCovDiff. Now everything is done through ExtDiff and a second
argument is added to it to represent the exterior covariant derivative.
23 Dec. 2013: Changed name ExtDiff by Diff. All the commands which contained ExtDiff in their
name contain now just Diff.
Changed name CoDiff by Codiff. All the commands which contained CoDiff in their name
contain now just Codiff.
Changed names DefDifferentialForm by DefDiffForm and UndefDifferentialForm by UndefDiffForm.
27 Dec. 2013: Added second argument to Lie representing a covariant derivative. LieDToCovD now trasforms Lie derivatives
of tensor valued differential forms into expressions containing the operator Lie.
Added DFormQ.
28 Dec. 2013: Adapted usage messages to the name changes mentioned above.
31 Dec. 2013: Changed the formatting of the operator Lie which is different from LieD. The operator Lie accepts a covariant
derivative as a second argument. The commutation rules of this operator have been adapted to this
new situation.
1 Jan. 2014: Added action of Int on Coframe and dx.
7 Jan. 2014: Added global variable $UseDimensionQ.
13 Jan. 2014: Implemented relation between Lie, Int and Basis objects.
15 Jan. 2014: Changed name "ExpandDiff" by "UseCartan".
Dropped $UseDimensionQ which is now replaced by UseDimensionStart[] and UseDimensionStop[].
16 Jan. 2014: Threaded Diff and UseCartan over equations and lists.
Diff[expr] is always automatically replaced by Diff[expr,PD].
18 Jan. 2014: Some name changes: new symbols are CartanD (Cartan Derivative) and CartanToDiff (transformation of the Cartan
derivative into an expression with the exterior derivative and the inner contraction by using the Cartan rule).
20 Jan. 2014: Removed DFormQ from xTerior.nb. It is no longer needed.
24 Jan. 2014: Added back dependency on the covariant derivative in Codiff. Codiff of xCoba basis objects yields zero.
26 Jan. 2014: Changed syntax of UseCartan when the covariant derivative argument is PD. See the on-line help of UseCartan.
Dropped ZeroFormQ.
27 Jan 2014: Changed name ExtCovDiff by ExtCovD.
28 Jan 2014: Coded UseDimensionStart and UseDimensionStop with xTensions. Patch submitted by José María.
* Released with version 0.8.5
12 Jul 2014: Added product CircleTimes.
12 Aug 2014: Added FindPotential.
15 Aug 2014: Added Inner contraction of basis objects.
29 Sep 2014: Added code to allow the inner contraction with covectors.
18 Oct 2014: Added relation of Wedge with respect to Times in GradeOfProduct, necessary when working with the latest xTensor.m.
Fixed the action of Int on Coframe and Frame.
18 Oct 2014: Started coding of support of CTensor in xTerior.
5 Nov 2014: Changed sign convention in the definition of Codiff.
6 Nov 2014: Changed sign in the definition of FormVarD to adapt to the new sign convention in Codiff.
7 Nov 2014: Added code to get Zero Riemann form.
23 Nov 2014: Fixed problem with the xTension DefTensorUseDimension.
7 Dec 2014: Fixed problems with the code of the exterior derivative. Thanks
to José for doing this.
16 Dec 2014: Corrected bug in UseDimensionStart
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2015
15 Aug 2015: corrected bug in CartanD.
19 Aug 2015: set version compatibility wit xTensor 1.1.2 and above.
* Released with version 0.9.0
21 Oct 2015: Fix in FindPotential for the case of 1-degree forms.
11 Feb. 2016: Added FormIntegrate and UseStokes by José.
26 Jul. Added code to compute the Hodge dual of scalar 0-forms.