This shows you the differences between two versions of the page.
|
documentation:ref:eliminatemetrics [2015/11/21 12:33] |
documentation:ref:eliminatemetrics [2015/11/21 12:33] (current) |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| + | ====== EliminateMetrics ====== | ||
| + | ---- | ||
| + | |||
| + | ====Description==== | ||
| + | * ''EliminateMetrics'' eliminates contractions with [[metric_tensor|metric tensors]] and [[Kronecker delta|Kronecker deltas]] in any part of expression. | ||
| + | |||
| + | |||
| + | * ''EliminateMetrics'' eliminates metrics for all types of indices, for who metric is defined. | ||
| + | |||
| + | * ''EliminateMetrics'' eliminates Kroneckers for all types of indices (even if no metric is defined for this type). | ||
| + | ====Examples==== | ||
| + | ---- | ||
| + | Eliminate metric tensor and Kronecker delta: | ||
| + | <sxh groovy; gutter: false> | ||
| + | println EliminateMetrics >> 'g_nm*A^m*d^n_a'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > A_a | ||
| + | </sxh> | ||
| + | ---- | ||
| + | Eliminate metric tensors in ''D'' dimensions: | ||
| + | <sxh groovy; gutter: false> | ||
| + | def t = ('g^mn*g^ab*g^gd*(p_g*g_ba + p_a*g_bg)*(p_m*g_dn + p_n*g_dm)').t | ||
| + | //eliminate metrics in D dimensions | ||
| + | println ((EliminateMetrics & 'd_a^a = D'.t) >> t) | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > 2*(1+D)*p^{d}*p_{d} | ||
| + | </sxh> | ||
| + | ---- | ||
| + | Eliminate metric tensors for different types of indices: | ||
| + | <sxh groovy; gutter: false> | ||
| + | def t = 'g_mn*A^mn + g_\\alpha\\beta*B^\\alpha\\beta + g_AB*C^AB'.t | ||
| + | println EliminateMetrics >> t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > A_{n}^{n}+B_{\beta}^{\beta}+C_{B}^{B} | ||
| + | </sxh> | ||
| + | ---- | ||
| + | ====See also==== | ||
| + | * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:list_of_transformations]] | ||
| + | * Related transformations: [[documentation:ref:expandandeliminate]] | ||
| + | * Related reference material: [[documentation:ref:metric_tensor]], [[documentation:ref:kronecker_delta]] | ||
| + | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/transformations/EliminateMetricsTransformation.html|EliminateMetricsTransformation]] | ||
| + | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/transformations/EliminateMetricsTransformation.java|EliminateMetricsTransformation.java]] | ||