einsteinify
Raise or lower indices of pairs which are both upper or lower.
In an expression containing dummy indices at the same position
(i.e. either both subscripts or both superscripts), raise or lower one of the
indices.ex:= A_{m} A_{m};
einsteinify(_);
\(\displaystyle{}A_{m} A_{m}\)
A_{m} A_{m}
\(\displaystyle{}A^{m} A_{m}\)
A^{m} A_{m}
ex:= A^{m} A^{m};
einsteinify(_);
\(\displaystyle{}A^{m} A^{m}\)
A^{m} A^{m}
\(\displaystyle{}A_{m} A^{m}\)
A_{m} A^{m}
If an additional argument is given to this algorithm, it instead inserts
"inverse metric" objects, with the name as indicated by the
additional argument.
{m,n}::Indices.
ex:= A_{m} A_{m};
einsteinify(_, $\eta$);
\(\displaystyle{}A_{m} A_{m}\)
A_{m} A_{m}
\(\displaystyle{}A_{m} A_{n} \eta^{m n}\)
A_{m} A_{n} \eta^{m n}
ex:= A^{m} A^{m};
einsteinify(_, $\eta$);
\(\displaystyle{}A^{m} A^{m}\)
A^{m} A^{m}
\(\displaystyle{}A_{m} A_{n} \eta^{m n}\)
A_{m} A_{n} \eta^{m n}
Note that the second form requires that there are enough dummy indices
defined through the use of
Indices
.