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 documentation:ref:fullysymmetrize [2015/11/21 10:44]poslavskysv [Examples] documentation:ref:fullysymmetrize [2015/11/21 12:33] Line 1: Line 1: - ====== FullySymmetrize ====== - ---- - ====Description==== - * ''​FullySymmetrize''​ makes expression symmetric with respect to all free indices - - * ''​FullySymmetrize[indices]''​ makes expression symmetric with respect to specified indices - - ==== Examples ==== - ---- - 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} - ​ - - ====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:​fullyantisymmetrize]]