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--- documentation:ref:diracsimplify [2015/11/20 20:05]
poslavskysv [Description]
+++ documentation:ref:diracsimplify [2015/11/21 12:33] (current)
@@ Line 17: / Line 17: @@
 ====Examples====
 ----
-Calculate trace of $\gamma$-matrices:
+Simplify different expressions:
-<sxh groovy; gutter: false>
+<sxh groovy; gutter: true>
 defineMatrices 'G_a', 'G5', Matrix1.matrix
-println DiracTrace >> 'Tr[G_a*G_b]'.t
+def dSimplify = DiracSimplify
+println dSimplify >> 'G_a*G^a'.t
 </sxh>
 <sxh plain; gutter: false>
-   > 4*g_ab
+   > 4
+</sxh>
+<sxh groovy; gutter: true; first-line: 4>
+println dSimplify >> 'G_a*G_b*G^a'.t
+</sxh>
+<sxh plain; gutter: false>
+   > -2*G_{b}
+</sxh>
+<sxh groovy; gutter: true; first-line: 5>
+println dSimplify >> 'G_a*G_b*G^a*G^b'.t
+</sxh>
+<sxh plain; gutter: false>
+   > -8
+</sxh>
+<sxh groovy; gutter: true; first-line: 6>
+println dSimplify >> 'G5*G_a*G_b*G^a*G^b*G5*G5'.t
+</sxh>
+<sxh plain; gutter: false>
+   > -8*G5
+</sxh>
+<sxh groovy; gutter: true; first-line: 7>
+println dSimplify >> 'G5*G_a*G_b*G^a*G5*G5'.t
+</sxh>
+<sxh plain; gutter: false>
+   > 2*G_{b}
 </sxh>
+----
+Simplify in different dimensions:
+<sxh groovy; gutter: true>
+defineMatrices 'G_a', 'G5', Matrix1.matrix
+def dSimplify = DiracSimplify[[Dimension: 'D']]
+println dSimplify >> 'G_a*G^a'.t
+</sxh>
+<sxh plain; gutter: false>
+   > D
+</sxh>
+<sxh groovy; gutter: true; first-line: 4>
+println dSimplify >> 'G_a*G_b*G^a'.t
+</sxh>
+<sxh plain; gutter: false>
+   > -(-2+D)*G_{b}
+</sxh>
+----
+Specify additional simplifications:
+<sxh groovy; gutter: true>
+defineMatrices 'G_a', 'G5', Matrix1.matrix
+def dSimplify = DiracSimplify[[Simplifications: 'p_a*k^a = s'.t]]
+println dSimplify >> 'p^b*k^c*G_a*G_b*G_c*G^a'.t
+</sxh>
+<sxh plain; gutter: false>
+   > 4*s
+</sxh>
 ====See also====
   * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:Setting up matrix objects]], [[documentation:guide:list_of_transformations]]
   * Related tutorials: [[documentation:tutorials:Compton scattering in QED]]
-  * Related transformations: [[documentation:ref:DiracTrace]], [[documentation:ref:DiracOrder]],  [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitarySimplify]], [[documentation:ref:UnitaryTrace]]
+  * Related transformations: [[documentation:ref:DiracTrace]], [[documentation:ref:spinorssimplify]], [[documentation:ref:DiracOrder]],  [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitarySimplify]], [[documentation:ref:UnitaryTrace]]
-  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.8/java-api//cc/redberry/physics/feyncalc/DiracSimplifyTransformation.html| DiracSimplifyTransformation]]
+  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/physics/feyncalc/DiracSimplifyTransformation.html| DiracSimplifyTransformation]]
   * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/DiracSimplifyTransformation.java|DiracSimplifyTransformation.java]]