a field theory motivated approach to computer algebra


Make an object symmetric in all indices.
Make an object symmetric in all indices. This information is then subsequently used by various algorithms, for instance canonicalise. An example:
A_{m n}::AntiSymmetric. B_{m n}::Symmetric. ex:=A_{m n} B_{m n};
\(\displaystyle{}A_{m n} B_{m n}\)
If you need symmetry in only a subset of all indices of a tensor, you need to use the TableauSymmetry property. A quick example:
C_{a n p}::TableauSymmetry(shape={2}, indices={1,2});
\(\displaystyle{}\text{Attached property TableauSymmetry to }C_{a n p}.\)
This gives indices 1 and 2 (counting starts from 0) the symmetry of the Young Tableau formed by one row of 2 boxes, which is the fully symmetric representation of the permutation group. Now you get, as expected,
ex:=C_{a n p} - C_{a p n};
\(\displaystyle{}C_{a n p}-C_{a p n}\)
For more information see the TableauSymmetry documentation.
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