Explicit result of inner contractions : Code " Int" in xTerior package

[Augniva Ray]

Hello community,

I have this issue working out explicitly an inner contraction.

1. Attached is a small code highlighting what I mean. 

2. I get the schematic result using " Int", as shown in the documentation. 

 But i want an explicit form given a vector field (\xi, in the code) and a polyform (\PhiT, in the code). 

3. I could manually do it, by coding what the inner contraction is supposed to do, using Coefficient [...], but I think there must be some code that internally does it anyway, which I do not know. 

Could someone let me know the code that does this automatically. 

It must be obvious, but I am missing something. 

Thanks,

A. 

[Juan Margalef]

I am not entirely familiar with the interaction between xTerior and xCoba, but it seems that Int is not trained to handle Diff[coordinate[]]. It is trained over dx[manifold]. Hence, a solution (although maybe not the optimal one) is to transform the former into the latter using the rule:

rule = {Diff[\[Alpha][]] -> dx[M4][{1, ch1}],
  Diff[\[Theta][]] -> dx[M4][{2, ch1}],
  Diff[\[Phi]1[]] -> dx[M4][{3, ch1}],
  Diff[\[Phi]2[]] -> dx[M4][{4, ch1}]}

Then 

Int[\[Xi][a]][Diff[\[Phi]1[]] /. rule]  returns b1
Int[\[Xi][a]][Diff[\[Phi]2[]] /. rule]  returns b2

Diff[\[CapitalPhi]T] - Int[\[Xi][a]][\[CapitalPhi]T /. rule] /.
  rule // Simplification returns 0

I hope this helps!

[Augniva Ray]

Hi Juan,

this works wonderfully. Thanks.

Also, thanks for the plausible clarification as to why it might not have been working in the first place. 

(So doubly thanks. )

A. 

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