====== 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]]