====== ExpandAndEliminate ======
----
====Description====
  * ''ExpandAndEliminate'' expands out product of sums and positive integer powers and permanently eliminates metric and Kronecker deltas.


  * ''ExpandAndEliminate'' is equivalent to sequential applying ''Expand & EliminateMetrics'' but works faster since applies ''EliminateMetrics'' at each level of expand procedure.


  * ''ExpandAndEliminate'' is equal to ''Expand[EliminateMetrics] & EliminateMetrics''.


  * When no metric tensors or Kronecker deltas involved, ''ExpandAndEliminate'' works same as ''Expand''.

  * ''ExpandAndEliminate[simplifications]'' or ''%%ExpandAndEliminate[[Simplifications: simplifications]]%%'' will apply additional simplifications at each level of expand procedure

====Examples====
----
Expand product of sums and eliminate metrics:
<sxh groovy; gutter: false>
def t = '(A_a*g_mn + A_m*g_an + A_n*g_am)*(A^a*g^mn + A^m*g^an + A^n*g^am)'.t
println ExpandAndEliminate >> t
</sxh>
<sxh plain; gutter: false>
   > 6*A_{n}*A^{n}+3*d^{n}_{n}*A_{m}*A^{m}
</sxh>


----
When no metric tensors or Kronecker deltas involved, ''ExpandAndEliminate'' works same as ''Expand'':
<sxh groovy; gutter: false>
println Expand >> '(A_m^m + 1)**3'.t
</sxh>
<sxh plain; gutter: false>
   > 3*A_{m}^{m}*A_{a}^{a}+A_{m}^{m}*A_{a}^{a}*A_{b}^{b}+1+3*A_{b}^{b}
</sxh>


----
====Details====
''ExpandAndEliminate'' is equivalent to sequential applying ''Expand & EliminateMetrics'' but works faster since it applies ''EliminateMetrics'' at each level of expand procedure. One can check the advantages of ''ExpandAndEliminate'' in the following example with random tensors:
<sxh groovy; gutter: false>
//create random generator, which generates 
// random tensors consisting of metric and A_m
def randomTensor = new RandomTensor()
randomTensor.clearNamespace()
randomTensor.addToNamespace('g_mn'.t, 'A_m'.t)

def a, b
//loop to warm up JVM 
for (def i in 0..1000) {
    //next random tensor
    def t = randomTensor.nextTensorTree(4, 3, 8, '_a'.si)

    //this will typically 10 times faster
    timing {
        a = ExpandAndEliminate >> t
    }
    //than this
    timing {
        b = (Expand & EliminateMetrics) >> t
    }

    assert a == b
    println ''
}
</sxh>
The sample output will looks like:
<sxh plain; gutter: false>
Time: 14 ms.
Time: 88 ms.

Time: 52 ms.
Time: 553 ms.

Time: 40 ms.
Time: 577 ms.
</sxh>

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