====== Transformation ======
----

====Basics====

  * ''Transformation'' represents a transformation of expression; it is a super type for all transformations (e.g. [[Expand]] or [[EliminateMetrics]]).  

  * ''Transformation'' can be applied to expression using ''%%>>%%'' operator. 

  * A list of common useful transformations can be found at [[documentation:guide:list_of_transformations]] page.

  * Transformations can be combined using ''&'' operator; e.g. ''Expand & EliminateMetrics'' will first expand out products of sums and then eliminate metric tensors.

  * Applying ''Transformation'' using ''%%>>%%'' operator is equivalent to direct invocation of method  ''.transform(exp)''.

  * The ''Identity'' transformation does nothing (''expr == Identity %%>>%% expr'')
====Examples====
[[Expand]] is a ''Transformation'' that expands out product of sums:
<sxh groovy; gutter: false>
println Expand >> '(a+b)*(c+d)'.t
</sxh>
<sxh plain; gutter: false>
   > a*c + a*d + b*c + b*d
</sxh>
----
Expression ''lhs = rhs'' is both [[Tensor]] and ''Transformation'':
<sxh groovy; gutter: false>
println 'f_a[x_a] = x_a'.t >> 'g^b[z_a] = f^b[z^i]'.t
</sxh>
<sxh plain; gutter: false>
   > g^b[z_a] = z^b
</sxh>
----
Combine transformations using ''&'':
<sxh groovy; gutter: false>
def tr = Expand & EliminateMetrics
println tr >> '(g_ab*g_cd + g_ac*g_bd)*g^bc'.t
</sxh>
<sxh plain; gutter: false>
   > 2*g_{da}
</sxh>
----
One can define a custom transformation using [[documentation:guide:programming_with_redberry#functions|closures]]:
<sxh groovy; gutter: false>
def customTr = { expr -> 2*expr } as Transformation
println customTr >> 'z + t'.t
</sxh>
<sxh plain; gutter: false>
   > 2*(z + t)
</sxh>
Define transformation that inverts indices:
<sxh groovy; gutter: false>
def tr = { expr ->
    //invert indices
    (expr.indices % expr.indices.inverted) >> expr
} as Transformation
println tr >> 'f_ab^cd'.t
</sxh>
<sxh plain; gutter: false>
   > f^ab_cd
</sxh>

====See also====
  * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:list_of_transformations]]
  * Related reference material: [[documentation:ref:tensor]]
  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/transformations/Transformation.html|Transformation]]
  * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/transformations/Transformation.java|Transformation.java]]