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documentation:ref:fullysymmetrize [2015/11/21 10:42] poslavskysv [Examples] |
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| - | ====== 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: | ||
| - | <sxh groovy; gutter: false> | ||
| - | println FullySymmetrize >> 'f_abc'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (1/6)*f_{bac}+(1/6)*f_{cab}+(1/6)*f_{abc}+(1/6)*f_{bca}+(1/6)*f_{acb}+(1/6)*f_{cba} | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: false> | ||
| - | println FullySymmetrize >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (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} | ||
| - | (1/3)*f_{iab}*f^{i}_{cd}+(1/3)*f_{iad}*f^{i}_{bc}+(1/3)*f_{iac}*f^{i}_{bd} | ||
| - | </sxh> | ||
| - | ---- | ||
| - | Symmetrize only with respect to particular indices: | ||
| - | <sxh groovy; gutter: false> | ||
| - | println FullySymmetrize['_ae'.si] >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > f_{bacd}*t^{dc}_{e}+f_{becd}*t^{dc}_{a}+(1/2)*f_{ebcd}*t^{cd}_{a} | ||
| - | +(1/2)*f_{abcd}*t^{cd}_{e} | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | Symmetries will be taken into account: | ||
| - | <sxh groovy; gutter: false> | ||
| - | println FullySymmetrize >> 'f_abc'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (1/6)*f_{bac}+(1/6)*f_{cab}+(1/6)*f_{abc}+(1/6)*f_{bca}+(1/6)*f_{acb}+(1/6)*f_{cba} | ||
| - | </sxh> | ||