====== FullyAntiSymmetrize ======
----
====Description====

  * ''FullyAntiSymmetrize'' makes expression antisymmetric with respect to all free indices

  * ''FullyAntiSymmetrize[indices]'' makes expression antisymmetric with respect to specified indices

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

----
Symmetries will be taken into account:
<sxh groovy; gutter: false>
setSymmetric 'f_abc'
println FullyAntiSymmetrize >> 'f_iab*f^i_cd'.t
</sxh>
<sxh plain; gutter: false>
   > 0
</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:fullysymmetrize]]