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--- documentation:ref:simpleindices [2015/11/21 12:33]
+++ documentation:ref:simpleindices [2015/11/21 12:33] (current)
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+====== SimpleIndices ======
+----
+====Basics====
+''SimpleIndices'' represents indices of [[SimpleTensor]] and [[TensorField]]. It inherits all properties of [[Indices]] but does not sort indices., so indices in ''SimpleIndices''  appear exactly in that order as defined by the user:
+<sxh groovy; gutter: false>
+def indices = '_pqrs^sp'.si
+println indices
+</sxh>
+<sxh plain; gutter: false>
+   > _pqrs^sp
+</sxh>
+On the other hand, since indices of different [[IndexType|types]] have different mathematical nature, [[SimpleIndices]] are sorted according to the type (preserving relative ordering of indices of same type):
+<sxh groovy; gutter: false>
+println '_{mn}^{\\beta\\alpha}_{ba\\alpha}'.si
+</sxh>
+<sxh plain; gutter: false>
+   > _{mnba}^{\beta\alpha}_{\alpha}
+</sxh>
+All properties and methods of ''SimpleIndices'' leaves the relative ordering of indices unchanged.
+''SimpleIndices'' has ''.symmetries'' property which allows to define their permutational symmetries.
+====Features====
+Since ''SimpleIndices'' is a subtype of [[Indices]], it inherits all its properties. However,  in contrast to [[Indices]], ''SimpleIndices'' and all its properties and methods preserve the relative ordering of indices.
+Consider examples. Parse ''SimpleIndices'' from string:
+<sxh groovy; gutter: true>
+def indices = '^an_ab^m_pq^b'.si
+println indices
+</sxh>
+<sxh plain; gutter: false>
+   > ^{an}_{ab}^{m}_{pq}^{b}
+</sxh>
+Get just free indices:
+<sxh groovy; gutter: true; first-line: 3>
+println indices.free
+</sxh>
+<sxh plain; gutter: false>
+   > ^{nm}_{pq}
+</sxh>
+Invert indices:
+<sxh groovy; gutter: true; first-line: 4>
+println indices.inverted
+</sxh>
+<sxh plain; gutter: false>
+   > _{an}^{ab}_{m}^{pq}_{b}
+</sxh>
+Get only contravariant indices:
+<sxh groovy; gutter: true; first-line: 5>
+println indices.upper
+</sxh>
+<sxh plain; gutter: false>
+   > ^{anmb}
+</sxh>
+Get only covariant indices:
+<sxh groovy; gutter: true; first-line: 6>
+println indices.lower
+</sxh>
+<sxh plain; gutter: false>
+   > _{abpq}
+</sxh>
+Parse indices with multiple types:
+<sxh groovy; gutter: true>
+def indices = '^AB_pqrs^C_A^sp'.si
+println indices
+</sxh>
+<sxh plain; gutter: false>
+   > _{pqrs}^{spABC}_{A}
+</sxh>
+Get just Latin upper case:
+<sxh groovy; gutter: true; first-line: 3>
+println indices.getOfType(LatinUpper)
+</sxh>
+<sxh plain; gutter: false>
+   > ^{ABC}_{A}
+</sxh>
+Get first index:
+<sxh groovy; gutter: true; first-line: 4>
+println indices[0].toStringIndex()
+</sxh>
+<sxh plain; gutter: false>
+   > _{p}
+</sxh>
+Get first Latin upper index:
+<sxh groovy; gutter: true; first-line: 5>
+println indices[LatinUpper, 0].toStringIndex()
+</sxh>
+<sxh plain; gutter: false>
+   > ^{A}
+</sxh>
+Get several indices at a time:
+<sxh groovy; gutter: true; first-line: 6>
+println indices[1, 3, 4]
+</sxh>
+<sxh plain; gutter: false>
+   > _{qs}^{s}
+</sxh>
+Get range:
+<sxh groovy; gutter: true; first-line: 7>
+println indices[1..4]
+</sxh>
+<sxh plain; gutter: false>
+   > _{qrs}^{s}
+</sxh>
+As one can see, all methods in the above examples return indices which have same relative ordering as in the initial object.
+====Symmetries====
+Symmetries can be attached to a single ''SimpleIndices'' object by using ''.symmetry'' property:
+<sxh groovy; gutter: false>
+def indices = '_abcdef'.si
+indices.symmetries.addSymmetry([[0, 1], [2, 3]].p)
+indices.symmetries.addSymmetry([[0, 3, 5]].p)
+println indices.symmetries.permutationGroup.order()
+</sxh>
+<sxh plain; gutter: false>
+   > 60
+</sxh>
+Symmetries of simple indices can be used in transformations like [[Symmetrize]] or other methods like [[GenerateTensor]] or [[Reduce]].
+The ''.symmetries'' property return a container of [[documentation:ref:permutation| permutations]] and a corresponding [[PermutationGroup]]. The latter can be accessed by taking ''.permutationGroup'' property.
+It should be noted, that when specifying symmetries of simple tensors like
+<sxh groovy; gutter: true>
+'f_abc'.t.indices.symmetries.addSymmetry( [1, 0].p )
+</sxh>
+these symmetries will be automatically attached to indices of all instances of tensor ''f_abc'', i. e. ''f_pqr'' or ''f_a^a_y'' etc.:
+<sxh groovy; gutter: true;first-line: 2>
+println 'f_pq^i'.t.indices.symmetries.permutationGroup
+</sxh>
+<sxh plain; gutter: false>
+   > Group( +[[0, 1]] )
+ </sxh>
+On the other hand, when specifying symmetries of "detached" indices:
+<sxh groovy; gutter: false>
+def ind = '_abc'.si
+ind.si.indices.symmetries.addSymmetry( [1, 0].p )
+</sxh>
+they will be attached just to the particular object (''ind'' in the above example).
+====See also====
+  * Related guides: [[documentation:guide:tensors_and_indices]], [[documentation:guide:symmetries_of_tensors]]
+  * Reference material: [[documentation:ref:indices]], [[documentation:ref:indextype]], [[documentation:ref:simpletensor]], [[documentation:ref:tensorfield]], [[documentation:ref:permutation]], [[documentation:ref:symmetrize]], [[documentation:ref:generatetensor]], [[documentation:ref:reduce]], [[documentation:ref:permutationgroup]]
+  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/indices/SimpleIndices.html| SimpleIndices]]
+  * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/indices/SimpleIndices.java|SimpleIndices.java]]