gives the list of independent components of an array of dimensions dims with the symmetry sym.
- The dimensions dims must be given as a list of positive integers.
- The symmetry sym must be compatible with the list of dimensions dims.
- SymmetrizedIndependentComponents generalizes the combinatorial construction of subsets and multisets, the former corresponding to antisymmetry and the latter to symmetry.
Examplesopen allclose all
This is an array with symmetry:
These are its independent components:
Extract the values of the independent components:
In an array with no symmetry, all components are independent:
Independent components of a rank-4 array whose symmetry is generated by a cycle:
Same situation, but having the generator with negative phase:
Properties & Relations (5)
A skew-symmetric array in dimension is zero if its depth is larger than the dimension, and hence there are no independent components:
Independent components under rank- antisymmetry in dimension dim are equivalent to the list of -subsets of Range[dim]:
Independent components under rank- symmetry in dimension dim are equivalent to the list of -multisets of Range[dim]:
Given an array with symmetry, the values of its independent components can be extracted in several forms:
The computation of independent components can be simulated using representatives of the orbits of components under Permute action:
Wolfram Research (2012), SymmetrizedIndependentComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetrizedIndependentComponents.html.
Wolfram Language. 2012. "SymmetrizedIndependentComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymmetrizedIndependentComponents.html.
Wolfram Language. (2012). SymmetrizedIndependentComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetrizedIndependentComponents.html