Strange error possibly related to the Invar database

[Daniel Mahler]

All of the following is in the same notebook:

Needs["xAct`xTras`"]

In[6]:= DefManifold[S2, 2, IndexRange[a, c]]

DefMetric[1, met2[-a, -b], CD2, {";", "\[Del]"}, PrintAs -> "g"]

In[8]:= FullSimplification[][NoScalar[EulerDensity[CD2]]]

Out[8]= RicciScalarCD2[]

So far so good

In[9]:= DefManifold[S3, 3, IndexRange[d, h]]

DefMetric[1, met3[-d, -e], CD3, {";", "\[Del]"}, PrintAs -> "g"]

In[11]:= FullSimplification[][NoScalar[EulerDensity[CD3]]]

During evaluation of In[11]:= ToCanonical::noident: Unknown expression not canonicalized: EulerDensity[CD3,3] .

During evaluation of In[11]:= ToCanonical::noident: Unknown expression not canonicalized: EulerDensity[CD3,3] .

During evaluation of In[11]:= ToCanonical::noident: Unknown expression not canonicalized: EulerDensity[CD3,3] .

During evaluation of In[11]:= General::stop: Further output of ToCanonical::noident will be suppressed during this calculation. >>

Out[11]= EulerDensity[CD3, 3]

Mathematica seems to have forgotten the definition of EulerDensity

In[12]:= DefManifold[S4, 4, IndexRange[i, p]]

DefMetric[1, met4[-i, -j], CD4, {";", "\[Del]"}, PrintAs -> "g"]

In[14]:= FullSimplification[][NoScalar[EulerDensity[CD4]]]

During evaluation of In[14]:= RInv::nodatabase: Can't find the Invar database. You can download it from http://www.xact.es/Invar/.

Out[14]= $Aborted

Now it has forgotten the location of the Invar database which it used in input 8.

Inputs 12 and 14 do work if the previous inputs are removed.

Can anyone suggest what the problem might be.

I am using Linux Home Edition Mathematica 10.0.2 with xAct-1.1.1.

I am also attaching the notebook illustrating this problem.

thanks

Daniel

[Teake Nutma]

Hi Daniel,

The Euler densities are only defined for even-dimensional manifolds; hence in three dimensions EulerDensity[CD3, 3] stays unevaluated.
As for the Invar database, the two-dimensional Euler density is so simple (it's just the Ricci scalar) that the Invar database isn't needed. For simplifying the four-dimension density it is needed however, which seems to suggest that you haven't yet installed it (it comes separate from the main xAct bundle).

Best,

Teake

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[Daniel Mahler]

Hi Teake,

I have installed the Invar DB.

 $ ls -l ~/.Mathematica/Applications/xAct/Invar/Riemann/

total 24

drwxr-xr-x 2 mahler mahler 4096 Jan 29  2008 1

drwxr-xr-x 2 mahler mahler 4096 Feb  5  2008 2

drwxr-xr-x 2 mahler mahler 4096 Jan 29  2008 3

drwxr-xr-x 2 mahler mahler 4096 Feb  7  2008 4

drwxr-xr-x 2 mahler mahler 4096 Feb  4  2008 5_4

drwxr-xr-x 2 mahler mahler 4096 Feb  4  2008 6_4

I also able to evaluate the Gauss-Bonnet term tutorial notebook that comes with the distribution.

That used to throw an error before I realized I had to install the Invar DB.

thanks

Daniel

[Daniel Mahler]

I also able to evaluate the Gauss-Bonnet term tutorial notebook that comes with the distribution.

That used to throw an error before I realized I had to install the Invar DB.

I could have sworn this worked at one point, but it does not work now,  so it may be a red herring.

thanks

Daniel