Cannot compute the Hodge dual of 1

[Fernando Saldanha]

I am learning about the xTerior package with the video 

https://www.youtube.com/watch?v=5qqiem8m8wg

20 minutes into the video I got in trouble (everything was working well prior to that). 

I ran 

Hodge[metricCyl] @ 1

and got 

*[1]

as expected. However, the next command

ToValues @ ExpandHodgeDual[%, dx[M3], metricCyl]

returned the same thing: *[1]

It should have returned an explicit 3-form as in the video.

Just prior to that the command 

ToValues @ ExpandHodgeDual[%, dx[M3], metricCyl]

had worked fine on an expression like * d[rho]  (where rho stands for the greek letter), returning an explicit 2-form.

Any help will be greatly appreciated.

[Alfonso Jacinto García Parrado Gómez Lobo]

Hi,

to fix this problem please go to the line 489 of the file xTerior.m and replace all the code defining ExpandHodgeDual1 (lines 489-495) by the following code:

ExpandHodgeDual1[expr_,(coframe:(Coframe|dx))[mani_?ManifoldQ],met_]:=
expr/.{HoldPattern[Hodge[met][form:Wedge[coframe[mani][_]..]]|form:Hodge[met][coframe[mani][_]]]:>With[{dim=DimOfMetric[met],n=Length[form],inds=Sequence@@@List@@form},
With[{dummies=DummyIn/@ConstantArray[VBundleOfMetric[met],dim-n]},
1/(dim-n)!epsilon[met]@@Join[inds,ChangeIndex/@dummies]Wedge@@(coframe[mani]/@dummies)
]
],HoldPattern[Hodge[met][form_]]:>With[{dim=DimOfMetric[met]},
With[{dummies=DummyIn/@ConstantArray[VBundleOfMetric[met],dim]},
form/(dim)!epsilon[met]@@(ChangeIndex/@dummies)Wedge@@(coframe[mani]/@dummies)
]
]/;(Deg[form]===0)};


If you still experience the problem, please let me know.

Thanks for your interest in xTerior.


Alfonso.

---

From: xa...@googlegroups.com [xa...@googlegroups.com] on behalf of Fernando Saldanha [fsal...@gmail.com]
Sent: Thursday, August 25, 2016 4:47 AM
To: xAct Tensor Computer Algebra
Subject: [xAct: 1856] Cannot compute the Hodge dual of 1

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