====== Indices ====== ---- ====Basics==== ''Indices'' represents indices of tensor. ''Indices'' is a simple container of single indices. For all types of tensors except [[SimpleTensor]] and [[TensorField]], ''Indices'' are always sorted in some predefined way (e.g. first upper then lower, first Latin then Greek, in each group indices sorted in lexicographical order etc.): def indices = '^AB_pqrs^C_A^sp'.i println indices > ^{psABC}_{pqrsA} The indices of [[SimpleTensor]] and [[TensorField]] are [[SimpleIndices]] --- a subtype of ''Indices'' that are not sorted. At the low-level, Redberry stores each single index as 32-bit integer that encodes all information about index: state, type and name (serial number in the alphabet). Within a particular index type, there are $2^{16}$ possible names, which can be inputted using the subscript: def indices = 'X_{\\mu_3 a_{122} a_1 b_9}'.i println indices > _{a_{1}b_{9}a_{122}\mu_{3}} ====Features==== Here is a list of common ''Indices'' properties and methods:

`.free`	free indices
`.inverted`	inverted indices
`.upper`	contravariant indices
`.lower`	covariant indices
`.getOfType(type)`	sub-indices of specified type
`.size()`	number of indices
`[i]`	i-th index
`[i..j]`	indices from i-th (inclusive) to j-th (exclusive)
`[i, j, k]`	i, j, k-th indices etc.
`[type, i]`	i-th index of type type

Consider examples. Parse indices from string: def indices = '^an_ab^m_pq^b'.i println indices > ^{abmn}_{abpq} Get just free indices: println indices.free > ^{mn}_{pq} Invert indices: println indices.inverted > ^{abpq}_{abmn} Get only contra variant indices: println indices.upper > ^{abmn} Get only covariant indices: println indices.lower > _{abpq} Parse indices with multiple types: def indices = '^AB_pqrs^C_A^sp'.i println indices > ^{psABC}_{pqrsA} Get just Latin upper case: println indices.getOfType(LatinUpper) > ^{ABC}_{A} Get first index: println indices[0].toStringIndex() > ^{p} Get first Latin upper index: println indices[LatinUpper, 0].toStringIndex() > ^{A} Get several indices at a time: println indices[1, 3, 4] > ^{sBC} Get range: println indices[1..4] > ^{sABC} As one can see, all methods in the above examples return also sorted indices. ====Creating indices==== Get indices of tensor: println 't_ba*f^dc'.t.indices > ^cd_ab Parse indices from string using ''.i'' property: println '_ba^dc'.i > ^cd_ab Convert array of single indices into ''Indices'': println( [0, 1, 2, 3.invert()] as Indices ) > ^d_abc Concatenate several ''Indices'' objects: println ( '_abc'.i + '^cad'.i ) > ^{acd}_{abc} ====See also==== * Related guides: [[documentation:guide:tensors_and_indices]] * Reference material: [[documentation:ref:simpleindices]], [[documentation:ref:tensor]], [[documentation:ref:indextype]] * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/indices/Indices.html| Indices]] * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/indices/Indices.java|Indices.java]]