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: 

println FullyAntiSymmetrize >> 'f_abc'.t

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

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

   > -(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}

Antisymmetrize only with respect to particular indices: 

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

  > (1/2)*t^{cd}_{e}*f_{abcd}-(1/2)*t^{cd}_{a}*f_{ebcd}

Symmetries will be taken into account: 

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

   > 0

See also