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--- documentation:ref:indextype [2015/11/21 12:33]
+++ documentation:ref:indextype [2015/11/21 12:33] (current)
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+====== IndexType ======
+----
+====Description====
+''IndexType'' represents a type of a single index. It encodes mathematical nature of indices with different types (e.g. Lorentz, SU(N) etc.).  One can print all available index types as follows:
+<sxh groovy; gutter: false>
+println IndexType.values()
+</sxh>
+<sxh plain; gutter: false>
+   > [LatinLower, LatinUpper, GreekLower, GreekUpper, Matrix1, Matrix2,
+      Matrix3, Matrix4]
+</sxh>
+If two indices have different types, then they have different mathematical nature. Thus, for example, two tensors ''f_ab'' and ''f_AB'' have different mathematical nature and one can not rename indices of tensor ''f_ab'' to ''_AB''. This, in turn, enables us to associate different space dimensions with different index types:
+<sxh groovy; gutter: false>
+//dimension for Latin lower case indices
+def dimLower = 'd^a_a = X'.t
+//dimension for Latin upper case indices
+def dimUpper = 'd^A_A = Y'.t
+//expression contains both lower and upper case indices
+def t = 'g_ab*g^ab + g_AB*g^AB'.t
+t = (EliminateMetrics & dimLower & dimUpper) >> t
+println t
+</sxh>
+<sxh plain; gutter: false>
+   > X + Y
+</sxh>
+By default, all types except ''Matrix'' are  metric, and a corresponding [[documentation:ref:metric_tensor|metric tensor]] is set up (''g_ab'' for ''LatinLower'', ''g_\\alpha\\beta'' for Greek lower etc.).
+In order to obtain ''IndexType'' of a particular index one can use ''.type'' property; in order to check whether ''IndexType'' is metric, one can use ''isMetric()'' method:
+<sxh groovy; gutter: false>
+def indices = '''_{a}^{A \\alpha}_{a'} '''.si
+println indices.collect { [[type: it.type, metric: it.type.isMetric()]] }
+</sxh>
+<sxh plain; gutter: false>
+   > [[[type:LatinLower, metric:true]], [[type:LatinUpper, metric:true]],
+        [[type:GreekLower, metric:true]], [[type:Matrix1, metric:false]]]
+</sxh>
+====Available types====
+The possible values of ''IndexType'' are:
+<html>
+<center>
+<table style="width:600px;" cellpadding="10">
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><b>IndexType</b></td>
+  <td valign="top" align="center" style="padding: 15px; border: 1px solid gray;"><b>Description</b></td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>LatinLower</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Latin lower case indices from <code>a</code> to <code>z</code> and subscripted like <code>a_{12}</code> etc. </td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>LatinUpper</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Latin upper case indices from <code>A</code> to <code>Z</code> and subscripted like <code>X_{12}</code> etc. </td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>GreekLower</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Greek lower case indices like <code>\\alpha</code>, <code>\\theta</code> and subscripted like <code>\\rho_{123}</code> etc. </td>
+  <tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>GreekUpper</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Greek upper case indices like <code>\\Lambda</code>, <code>\\Theta</code> and subscripted like <code>\\Psi_{123}</code> etc. Note, that some letters are excluded since they have same UTF8 representation as Latin letters (e.g. capital alpha to beta). </td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>Matrix1</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Latin lower case indices with strokes from <code>a'</code> to <code>z'</code> and subscripted like <code>a'_{12}</code> etc. </td>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>Matrix2</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Latin upper case indices with strokes like <code>A'</code> or <code> E'_{12}</code>. </td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>Matrix3</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Greek lower case indices with strokes like <code>\\alpha'</code> or <code>\\theta'_{12}</code>. </td>
+</tr>
+<tr>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;"><code>Matrix4</code></td>
+  <td valign="top" style="padding: 15px; border: 1px solid gray;">Greek upper case indices with strokes like <code>\\Lambda'</code> or <code>\\Psi'_{12}</code>. </td>
+</tr>
+</tr>
+</table>
+</center>
+</html>
+By default all ''Matrix'' index types are used for [[documentation:guide:setting_up_matrix_objects|matrix indices]] and there is no metric specified for indices of ''Matrix'' types.
+=====See also=====
+  * Related guides: [[documentation:guide:tensors_and_indices]]
+  * Reference material: [[documentation:ref:indices]], [[documentation:ref:simpletensor]], [[documentation:ref:simpleindices]], [[documentation:ref:metric_tensor]]
+  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/indices/IndexType.html| IndexType]]
+  * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/indices/IndexType.java|IndexType.java]]