problem in contracting with metric in makerule

[NUR JAMAN]

Hi,
I am attaching a model of calculation where I have made use of several rules . In my rule there is conversion of some tensor into other tensor and this should hold in  the same way both for lower and upper index. Now this is working fine, but the metric contraction is not working for those quantity which are in the denominator of my expression , Also other rule are not applying in the denominator part as you will see from the attached file.  I don't know where I am mistaking .

Thanks

[Thomas Bäckdahl]

Hi!

ContractMetric is used in MakeRule, but there the settings will not allow upper derivatives. To allow this everywhere use

SetOptions[ContractMetric, AllowUpperDerivatives -> True]

I would also suggest to use Scalar when you divide by something with indices in it. For instance

1/Sqrt[1 + Scalar[CD[-a]@pi[] CD[a]@pi[]]]

The last line in your example works best if you do
expr4=expr3//.rule2

Then it applies the rule repeatedly.

There is also a way to work with equations instead of expressions, but as that is just a matter of taste I am not explaining it now unless you ask for it.

I hope this helps.

Regards
Thomas

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[NUR JAMAN]

Hi TB,
Thanks for the reply, it is now working . And  of course I want to be familiar with the alternative ways of handling these.

Thanks again