({{, (RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules])[sa] 
returns a list of rules (Subscript[pos, i])->(Subscript[val, i]) of the symmetrized array sa.}, {, (RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules])[a,sym]
returns a list of rules (Subscript[pos, i])->(Subscript[val, i]) of the array a after being symmetrized with symmetry sym.}})

OpenersNotesSection(Spacer1)Details

The rules returned by (RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules]) are meant to be applied only to the independent components, as returned by (RefLink[SymmetrizedIndependentComponents, paclet:ref/SymmetrizedIndependentComponents]).

(RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules])[sa] returns a list describing the nonzero independent components. The last element of the list is always {_,_,…}->0.

(RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules])[a] for a normal or sparse array a is automatically converted into (RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules])[a,{}].

OpenersPrimaryExamplesSection(Spacer1)Examples  (6)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Take a symmetrized array:

sa=SymmetrizedArray[pos_:>RandomInteger[10],{4,4,4},Antisymmetric[{1,2,3}]]

This is a list with its independent component rules:

SymmetrizedArrayRules[sa]

Independent rules of a matrix after antisymmetrization:

SymmetrizedArrayRules[{{a,b},{c,d}},Antisymmetric[{1,2}]]

OpenersExampleSection1(Spacer1)Scope  (2)

For a symmetrized array, return the independent rules corresponding to the symmetry of the symmetrized array:

sa=SymmetrizedArray[{{1,1,1}->3,{1,2,2}->-2},{2,2,2},Symmetric[All]]

SymmetrizedArrayRules[sa]

For an ordinary array, specify the symmetry to be used to extract the independent components:

SymmetrizedArrayRules[{{a,b},{c,d}},Symmetric[{1,2}]]

Without a second argument, the identity symmetry is assumed:

SymmetrizedArrayRules[{{a,b},{c,d}}]

OpenersExampleSection3(Spacer1)Properties & Relations  (2)

If there is only one argument, and it is not a symmetrized array, then (RefLink[SymmetrizedArrayRules, paclet:ref/SymmetrizedArrayRules]) is equivalent to (RefLink[ArrayRules, paclet:ref/ArrayRules]):

SymmetrizedArrayRules[{{a,b},{c,d}}]

ArrayRules[{{a,b},{c,d}}]

For a symmetrized array, return the independent rules corresponding to the symmetry of the symmetrized array:

sa=SymmetrizedArray[{{1,1,1}->3,{1,2,2}->-2},{2,2,2},Symmetric[All]]

indeprules=SymmetrizedArrayRules[sa]

These are all the independent components and their values:

SymmetrizedIndependentComponents[{2,2,2},Symmetric[All]]

%/.indeprules

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[SymmetrizedArray, paclet:ref/SymmetrizedArray])  ▪  (RefLink[StructuredArray, paclet:ref/StructuredArray])  ▪  (RefLink[SymmetrizedIndependentComponents, paclet:ref/SymmetrizedIndependentComponents])  ▪  (RefLink[SymmetrizedDependentComponents, paclet:ref/SymmetrizedDependentComponents])  ▪  (RefLink[Symmetric, paclet:ref/Symmetric])  ▪  (RefLink[Antisymmetric, paclet:ref/Antisymmetric])}})}})

({{DocumentationFooterIconsRelatedTutorial.png, ({{Tutorials}, {▪(RefLinkPlain[Symbolic Tensors, paclet:tutorial/SymbolicTensors])}, {▪(RefLinkPlain[Tensor Symmetries, paclet:tutorial/TensorSymmetries])}, {▪(RefLinkPlain[Symmetrized Arrays, paclet:tutorial/SymmetrizedArrays])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Symbolic Tensors, paclet:guide/SymbolicTensors])}})}})