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| + | ====== EliminateDueSymmetries ====== | ||
| + | ---- | ||
| + | |||
| + | ====Description==== | ||
| + | * ''EliminateDueSymmetries'' removes parts of expression, which are zero because of the symmetries. | ||
| + | |||
| + | * ''EliminateDueSymmetries'' does not perform any structural simplifications (expand, eliminate metrics etc.), it is just using symmetries of expression. | ||
| + | |||
| + | ====Examples==== | ||
| + | |||
| + | Simplify expression where symmetric tensor is contracted with antisymmetric: | ||
| + | <sxh groovy; gutter: false> | ||
| + | setAntiSymmetric 'f_mn' | ||
| + | //g_mn is symmetric metric tensor | ||
| + | println EliminateDueSymmetries >> 'f_mn * g^mn'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > 0 | ||
| + | </sxh> | ||
| + | ---- | ||
| + | ''EliminateDueSymmetries'' also checks symmetries that follows from the structure of expressions: | ||
| + | <sxh groovy; gutter: false> | ||
| + | println EliminateDueSymmetries >> '(t_amn - t_anm) * g^mn'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > 0 | ||
| + | </sxh> | ||
| + | ---- | ||
| + | ''EliminateDueSymmetries'' works with expressions with arbitrary complexity: | ||
| + | <sxh groovy; gutter: false> | ||
| + | addSymmetry 'R_abc', -[1, 0, 2].p | ||
| + | addSymmetry 'A_ab', [1, 0].p | ||
| + | def t = '((R_abc*A_de + R_bde*A_ac)*A^ce + R_adb)*(A_mf*R^mad - A_fm*R^dma)'.t | ||
| + | println EliminateDueSymmetries >> t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > 0 | ||
| + | </sxh> | ||
| + | ---- | ||
| + | ''EliminateDueSymmetries'' applies to each part of expression: | ||
| + | <sxh groovy; gutter: false> | ||
| + | def t = 'F_mn + g_mn*(A^mn - A^nm)'.t | ||
| + | println EliminateDueSymmetries >> t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > F_mn | ||
| + | </sxh> | ||
| + | ---- | ||
| + | ====See also==== | ||
| + | * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:symmetries_of_tensors]], [[documentation:guide:list_of_transformations]] | ||
| + | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/core/transformations/EliminateDueSymmetriesTransformation.html|EliminateDueSymmetriesTransformation]] | ||
| + | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/transformations/EliminateDueSymmetriesTransformation.java|EliminateDueSymmetriesTransformation.java]] | ||