symmetrizes all symmetrizable covariant derivatives in expr.
SymmetrizeCovDs[expr, cd]
only symmetrizes the covariant derivative cd.
  • SymmetrizeCovDs only symmetrizes covariant derivatives that have been flagged as symmetrizable. This can be done by giving the option SymCovDQ -> True to DefCovD (or DefMetric) when the covariant derivative is defined.
  • Symmetrized covariant derivatives can be entered as e.g. CD[a,b,c,...][expr], and are symmetric in all indices on the derivative.
  • The following options can be given:
"UseCache"Truewhether or not to cache results
  • Possible settings for "UseCache" include:
Truecache results to speed up subsequent computations
Falsedon't cache results
  • With caching turned on, the first result takes longer to compute because it has to be written to the cache. Subsequent symmetrizations will be faster however.
  • The implementation of symmetrizing derivatives is exponentially complex in the number of derivatives. SymmetrizeCovDs has an optimized algorithm in the case when there is no torsion. Whenever there is torsion, a slower algorithm is used.
By default, symmetrizations are cached:
Subsequent symmetrizations are then faster:
But the first symmetrization was slower compared to when no cache is used: