[xTerior-Bug?] Issue with Diff[Hodge] when UseDimensionStart is activated

[Nils Marion]

Dear xAct community,

I ran into a strange behavior in xTerior that I definitely can not fully understand.

I’m working on a 4D manifold ( A4 ), with a scalar ( B0 ), a 2-form ( B2 ), and a metric ( g4 ).

Let me define Hstar = Hodge[g4][B2[ ] ^ Diff@B0[ ] ]. 
If I compute Diff@Hstar //ToCanonical, everything works fine.
However, when I activate UseDimensionStart[] to take into account the dimensionality of A4, the same expression returns the error:
"DimOfManifold: Unknown manifold AnyDependencies".
I have checked that all objects correctly return A4 when using DependenciesOf, so it does not seem to come from inconsistent manifold assignments.

Please find attached a minimal working example illustrating the issue..

Have a great day!

Nils

[Juan Margalef]

UseDimensionStart[] forces certain expressions to be zero when applying ToCanonical. It checks if expressions with Diff and Wedge have a degree higher than the dimension of the manifold. However, ToCanonical, canonicalizes from the "most nested" to the outside and once an expression has been canonicalized changes some heads (like Wedge for VerbatimProduct[Wedge]) to avoid "recanonicalazing". Like that, if it finds some Verbatim, it skips it. However, I think it is during this second round that UseDimensionStart[] doesn't know how to handle VerbatimProduct[Wedge]. One option would be to change UseDimensionStart[] to include this case but I think the easiest solution is to say that the dimension of AnyDependencies is infinity:

Unprotect[DimOfManifold];
DimOfManifold[xAct`xTensor`AnyDependencies] := Infinity;
Protect[DimOfManifold];

I am not sure if this would pose problems elsewhere, but for your purposes, I think is enough.