Mathematica Asked by Takoda on December 7, 2020
If I try to convert a tensor object to a CTensor
DefTensor[F[i, j], M, Antisymmetric[{i, j}]];
Fc = ToCTensor[F, {ch, ch}]
The output is
CTensor[{{F[{1, ch}, {1, ch}] , F[{1, ch}, {2, ch}] , F[{1, ch}, {3, ch}]},
{F[{2, ch}, {1, ch}] , F[{2, ch}, {2, ch}] , F[{2, ch}, {3, ch}]},
{F[{3, ch}, {1, ch}] , F[{3, ch}, {2, ch}] , F[{3, ch}, {3, ch}]}},
{ch, ch}, 0]
which is obviously not antisymmetric. I would have expected
CTensor[{{0 , F[{1, ch}, {2, ch}] , F[{1, ch}, {3, ch}]},
{-F[{1, ch}, {2, ch}] , 0 , F[{2, ch}, {3, ch}]},
{-F[{1, ch}, {3, ch}] , -F[{2, ch}, {3, ch}] , 0}},
{ch, ch}, 0]
How do I keep antisymmetry in the co-ordinate basis? Thank you!
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