====== 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: println IndexType.values() > [LatinLower, LatinUpper, GreekLower, GreekUpper, Matrix1, Matrix2, Matrix3, Matrix4] 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: //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 > X + Y 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: def indices = '''_{a}^{A \\alpha}_{a'} '''.si println indices.collect { [[type: it.type, metric: it.type.isMetric()]] } > [[[type:LatinLower, metric:true]], [[type:LatinUpper, metric:true]], [[type:GreekLower, metric:true]], [[type:Matrix1, metric:false]]] ====Available types==== The possible values of ''IndexType'' are:

IndexType	Description
`LatinLower`	Latin lower case indices from `a` to `z` and subscripted like `a_{12}` etc.
`LatinUpper`	Latin upper case indices from `A` to `Z` and subscripted like `X_{12}` etc.
`GreekLower`	Greek lower case indices like `\\alpha`, `\\theta` and subscripted like `\\rho_{123}` etc.
`GreekUpper`	Greek upper case indices like `\\Lambda`, `\\Theta` and subscripted like `\\Psi_{123}` etc. Note, that some letters are excluded since they have same UTF8 representation as Latin letters (e.g. capital alpha to beta).
`Matrix1`	Latin lower case indices with strokes from `a'` to `z'` and subscripted like `a'_{12}` etc.
`Matrix2`	Latin upper case indices with strokes like `A'` or `E'_{12}`.
`Matrix3`	Greek lower case indices with strokes like `\\alpha'` or `\\theta'_{12}`.
`Matrix4`	Greek upper case indices with strokes like `\\Lambda'` or `\\Psi'_{12}`.

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]]