FullySymmetrize

• FullySymmetrize makes expression symmetric with respect to all free indices

• FullySymmetrize[indices] makes expression symmetric with respect to specified indices

Symmetrize expression:

println FullySymmetrize >> 'f_abc'.t

   > (1/6)*f_{bac}+(1/6)*f_{cab}+(1/6)*f_{abc}+(1/6)*f_{bca}+(1/6)*f_{acb}+(1/6)*f_{cba}

println FullySymmetrize >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t

   > (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}

Symmetrize only with respect to particular indices:

println FullySymmetrize['_ae'.si] >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t

  > f_{bacd}*t^{dc}_{e}+f_{becd}*t^{dc}_{a}+(1/2)*f_{ebcd}*t^{cd}_{a}
       +(1/2)*f_{abcd}*t^{cd}_{e}

Symmetries will be taken into account:

setSymmetric 'f_abc'
println FullySymmetrize >> 'f_iab*f^i_cd'.t

   > (1/3)*f_{iad}*f^{i}_{bc}+(1/3)*f_{iac}*f^{i}_{bd}+(1/3)*f_{iab}*f^{i}_{cd}

• Related guides: Applying and manipulating transformations, Symmetries of tensors, Tensors and Indices, List of common transformations
• Related transformations: Symmetrize, FullyAntiSymmetrize