# Differences

This shows you the differences between two versions of the page.

 documentation:ref:fullyantisymmetrize [2015/11/21 10:47]poslavskysv created documentation:ref:fullyantisymmetrize [2015/11/21 12:33] 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]]