Why does MetricInBasis not define its own inverse rules

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Andrew Kovachik

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Jan 26, 2023, 2:54:29 PM1/26/23
to xAct Tensor Computer Algebra
Considering the following minimal example:

DefManifold[M, 4, IndexRange[a, q]]

DefMetric[-1, met[-a, -b], CD, PrintAs -> "g"]

DefChart[cartesian, M, {0, 1, 2, 3}, {t[], x[], y[], z[]},
 FormatBasis -> {"Partials", "Differentials"}, ChartColor -> Red]

flatmetriccart =
  CTensor[DiagonalMatrix[{-1, 1, 1, 1}], {-cartesian, -cartesian}, 0];

MetricInBasis[met, -cartesian, flatmetriccart]

I get a set of rules that define the lowered basis, but it does not infer what the inverse metric would be, which I think it should given that the raised metric should be its own inverse?

Cheers,
Anndrew


Jose

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Jan 26, 2023, 11:17:42 PM1/26/23
to xAct Tensor Computer Algebra
Hi again,

This post is essentially equivalent to


and was addressed there.

Cheers,
Jose.
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