SymmetrizedArrayRules
returns a list of rules posivali of the symmetrized array sa.
SymmetrizedArrayRules[a,sym]
returns a list of rules posivali of the array a after being symmetrized with symmetry sym.
Details
- The rules returned by SymmetrizedArrayRules are meant to be applied only to the independent components, as returned by SymmetrizedIndependentComponents.
- SymmetrizedArrayRules[sa] returns a list describing the nonzero independent components. The last element of the list is always {_,_,…}->0.
- SymmetrizedArrayRules[a] for a normal or sparse array a is automatically converted into SymmetrizedArrayRules[a,{}].
Examples
open all close allBasic Examples (2)
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}]]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}}]Properties & Relations (2)
If there is only one argument, and it is not a symmetrized array, then SymmetrizedArrayRules is equivalent to 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]]% /. indeprulesText
Wolfram Research (2012), SymmetrizedArrayRules, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetrizedArrayRules.html.
CMS
Wolfram Language. 2012. "SymmetrizedArrayRules." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymmetrizedArrayRules.html.
APA
Wolfram Language. (2012). SymmetrizedArrayRules. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetrizedArrayRules.html