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| + | ====== 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: | ||
| + | <sxh groovy; gutter: false> | ||
| + | println FullyAntiSymmetrize >> 'f_abc'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > (1/6)*f_{cab}-(1/6)*f_{bac}+(1/6)*f_{bca}-(1/6)*f_{acb}-(1/6)*f_{cba}+(1/6)*f_{abc} | ||
| + | </sxh> | ||
| + | <sxh groovy; gutter: false> | ||
| + | println FullyAntiSymmetrize >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > -(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} | ||
| + | </sxh> | ||
| + | ---- | ||
| + | Antisymmetrize only with respect to particular indices: | ||
| + | <sxh groovy; gutter: false> | ||
| + | println FullyAntiSymmetrize['_ae'.si] >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > (1/2)*t^{cd}_{e}*f_{abcd}-(1/2)*t^{cd}_{a}*f_{ebcd} | ||
| + | </sxh> | ||
| + | |||
| + | ---- | ||
| + | Symmetries will be taken into account: | ||
| + | <sxh groovy; gutter: false> | ||
| + | setSymmetric 'f_abc' | ||
| + | println FullyAntiSymmetrize >> 'f_iab*f^i_cd'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > 0 | ||
| + | </sxh> | ||
| + | |||
| + | ====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]] | ||