ToCanonical gives (seemingly) incorrect result on tensor with subvbundle indices

[hadroncfy]

Hi,

I'm having trouble working with product manifold. Here's a minimum example to show the problem I encountered: (note that the tensor R has the same sym group as the Riemann tensor)

DefManifold[M1, 1, {i, j, k, l}];

DefManifold[M2, 1, {a, b, c, d}];

DefManifold[M, {M1, M2}, {A1, B1, C1, D1}];

DefTensor[R[-A1, -B1, -C1, -D1], M, StrongGenSet[{1, 2, 3, 4}, GenSet[-Cycles@{1, 2}, -Cycles@{3, 4}, Cycles[{1, 3}, {2, 4}]
]]];

R[-A1, -i, -B1, -j] // ToCanonical // Print

It gives R[-A1, -B1, -i, -j], which doesn't seem correct since the second and third slot should be anti-symmetric. Am I doing anything wrong or it's an issue with xAct?

Thank you in advance for any help.

Kind regards.

[Jose]

Hi,

I think the problem here derives from the use of 1D manifolds. xAct assumes additional index-symmetries in this case, and this seems to be interfering with the canonicalization process in your example. I need to investigate why this is. In the meantime, you can deactivate the addition of those 1D symmetries doing this:

Clear[xAct`xTensor`Private`Symmetry1D]
xAct`xTensor`Private`Symmetry1D[sym_, inds_] := sym

Then M1 and M2 will be treated during canonicalization like manifolds of general dimension.

Thanks for reporting this.

Cheers,

Jose.