The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a fundamental component of special and general relativity (Misner et al. 1973, pp. 8489). Examples of index gymnastics include
(1)
 
(2)
 
(3)
 
(4)
 
(5)
 
(6)
 
(7)
 
(8)

(Misner et al. 1973, p. 85), where is the metric tensor, is the Kronecker delta, is a comma derivative, is the antisymmetric tensor part, and is the symmetric tensor part.