slot_asym
Anti-symmetrise or symmetrise an expression in indicated index slots
Anti-symmetrise or symmetrise (depending on the antisymmetric
flag) a product or tensor in the indicated indices,
where the indices are given as slot positions. This complements the asym
algorithm, which instead takes the
index names over which to (anti-)symmetrise.ex:=A_{m n} B_{p q};
AmnBpq
A_{m n} B_{p q}
slot_asym(_, [1,2]);
12AmnBpq−12AmpBnq
1/2 A_{m n} B_{p q} - 1/2 A_{m p} B_{n q}
If you want to symmetrise in the indicated objects instead, use the
antisymmetric=False
flag:ex:=A_{m n} B_{p q};
slot_asym(_, [1,2], antisymmetric=False);
AmnBpq
A_{m n} B_{p q}
12AmnBpq+12AmpBnq
1/2 A_{m n} B_{p q} + 1/2 A_{m p} B_{n q}