====== FullySymmetrize ======
----
====Description====

  * ''FullySymmetrize'' makes expression symmetric with respect to all free indices

  * ''FullySymmetrize[indices]'' makes expression symmetric with respect to specified indices

==== Examples ====
----
Symmetrize expression:
<sxh groovy; gutter: false>
println FullySymmetrize >> 'f_abc'.t
</sxh>
<sxh plain; gutter: false>
   > (1/6)*f_{bac}+(1/6)*f_{cab}+(1/6)*f_{abc}+(1/6)*f_{bca}+(1/6)*f_{acb}+(1/6)*f_{cba}
</sxh>
<sxh groovy; gutter: false>
println FullySymmetrize >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t
</sxh>
<sxh plain; gutter: false>
   > (1/3)*t^{dc}_{e}*f_{abcd}+(1/3)*t^{dc}_{a}*f_{ebcd}
      +(1/3)*t^{dc}_{e}*f_{bacd}+(1/3)*t^{dc}_{b}*f_{aecd}
      +(1/3)*t^{dc}_{b}*f_{eacd}+(1/3)*t^{dc}_{a}*f_{becd}
      +(1/6)*t^{cd}_{e}*f_{abcd}+(1/6)*t^{cd}_{a}*f_{ebcd}
      +(1/6)*t^{cd}_{e}*f_{bacd}+(1/6)*t^{cd}_{b}*f_{aecd}
      +(1/6)*t^{cd}_{b}*f_{eacd}+(1/6)*t^{cd}_{a}*f_{becd}
</sxh>
----
Symmetrize only with respect to particular indices:
<sxh groovy; gutter: false>
println FullySymmetrize['_ae'.si] >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t
</sxh>
<sxh plain; gutter: false>
  > f_{bacd}*t^{dc}_{e}+f_{becd}*t^{dc}_{a}+(1/2)*f_{ebcd}*t^{cd}_{a}
       +(1/2)*f_{abcd}*t^{cd}_{e}
</sxh>

----
Symmetries will be taken into account:
<sxh groovy; gutter: false>
setSymmetric 'f_abc'
println FullySymmetrize >> 'f_iab*f^i_cd'.t
</sxh>
<sxh plain; gutter: false>
   > (1/3)*f_{iad}*f^{i}_{bc}+(1/3)*f_{iac}*f^{i}_{bd}+(1/3)*f_{iab}*f^{i}_{cd}
</sxh>

====See also====
  * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:symmetries_of_tensors]], [[documentation:guide:tensors_and_indices]],  [[documentation:guide:list_of_transformations]]
  * Related transformations: [[documentation:ref:symmetrize]],  [[documentation:ref:fullyantisymmetrize]]