====== 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]]