Integration by parts using VarD

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Nitol Attar

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Jul 23, 2022, 3:10:55 PM7/23/22
to xAct Tensor Computer Algebra
Hello everyone,

I am trying to implement partial integrations and discard the total derivatives on an expression. Eventually it should give me only three terms replaced by the symmetric tensors I defined. I was using VarD to achieve it. But it is not working. Any suggestions, please? The notebook is uploaded.

VarDQ.nb

Sergi Sirera-Lahoz

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Feb 24, 2023, 8:44:47 AM2/24/23
to xAct Tensor Computer Algebra
Hi Nitol,

I'm not sure how you wanted to use VarD to integrate by parts and discard total derivtives but for that I use a simple rule like the following:

IBPrule1 = XX_*h[LI[1], aa_, bb_] CD[cc_]@CD[dd_]@h[LI[1], ee_, ff_] -> -CD[cc]@(XX*h[LI[1], aa, bb])*CD[dd]@h[LI[1], ee, ff]

or, more generally,

IBPrule2 = XX_*CD[cc_]@CD[dd_]@YY_ -> -CD[cc]@XX*CD[dd]@YY

Note that the indices are different (you use greek indices in your notebook so you'll have to change that)

Best,

Sergi

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