# Differences

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 — documentation:ref:fullyantisymmetrize [2015/11/21 12:33] (current) 2015/11/21 10:47 poslavskysv created 2015/11/21 10:47 poslavskysv created Line 1: Line 1: + ====== 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==== + * 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]]