Problem with RiemannSimplify

[Sukruti]

Hello,

The command RiemannSimplify works for some terms but not for others. The attached notebook can be seen for some examples. I have the following two questions.

1) How to know in general which kind of terms it works for and which ones it doesn't work for?

2) Is there any indirect way to make it work for the terms which it doesn't work for in the first, direct attempt?

Best,

Sukruti

[Jose]

Hi,

The Invar package requires a particular value of some of the configuration settings. If you just load Invar then note these messages:

<< xAct`Invar`
.......
** Option AllowUpperDerivatives of ContractMetric changed from False to True
** Option CurvatureRelations of DefCovD changed from True to False
** Variable $CommuteCovDsOnScalars changed from True to False

where I've removed all other uninteresting (for our purpose) messages.

But your notebook loads xTras, which undoes one of these settings:

<<xAct`xTras`

.......

** Option CurvatureRelations of DefCovD changed from False to True

and then I see your notebook is undoing another one:

In[]:= $CommuteCovDsOnScalars = True
Out[]= True

Those two things effectively break some of the cases of Invar, as you have found.

CurvatureRelations -> True is what makes contractions of Riemann become Ricci, etc. Invar wants to see only Riemann tensors.

So, either you work with only Invar, without loading xTras, or you set CurvatureRelations -> False in your call to DefMetric. And don't change the value of $CommuteCovDsOnScalars.'

Cheers,

Jose.

[Sukruti]

Dear Jose,

Thank you for explaining what the issue was. I tried your suggestions and both of them worked. This was very helpful.

Many thanks!

Cheers

Sukruti

[Sukruti]

Hello,

RiemannSimplify works fine for all Riemann scalar expressions whether or not they consist of the Levi-Civita tensor. But when using ReimannSimplify with Riemann tensorial expressions, I find that it does not work for the expressions consisting of the Levi-Civita tensor. The problem is illustrated in the attached notebook.

Is there a way to fix this problem?

Best,

Sukruti

[Barry Wardell]

Hi Sukruti,

Currently TInvar only supports dual invariants (involving the epsilon tensor) for scalars, the database of identities has not yet been produces for dual invariants with free indices. This may be addressed in a future version.

Regards,

Barry

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[Sukruti]

Hi Barry,

Thank you for your reply.

If possible, I’d like to sign up for a notification in case TInvar extends its support for dual invariants involving the Levi-Civita tensor in the future. I’m not sure whether such a notification system exists. If not, I’d be very grateful if you could kindly reply to this email when the update happens.

Many thanks!

Best,

Sukruti