# SymmetrizedDependentComponents

SymmetrizedDependentComponents[comp,sym]

gives the list of components that are equivalent to the component comp by the symmetry sym.

# Details • The component comp must be given as a list of positive integers.

# Examples

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## Basic Examples(1)

Components of a depth-3 array related by symmetry to component {1,3,5}:

Components vanishing by symmetry are also related to other components:

## Scope(2)

This is an array with symmetry:

These are the dependent components associated to component {1,1,2}:

The respective values coincide by symmetry:

In an array with no symmetry, all components are independent:

## Properties & Relations(4)

Using Symmetric, SymmetrizedDependentComponents is essentially equivalent to Permutations:

SymmetrizedDependentComponents allows permuting only some elements:

SymmetrizedDependentComponents is an orbit computation under Permute action with the group associated to the symmetry permutations:

Take a symmetry for a depth-4 array:

There are 55 independent components in dimension 5:

Compute the respective dependent components and flatten the result:

The remaining components are all zero by symmetry:

The relationship of the values of the dependent components to each other depends on the phases of the symmetry generators. For antisymmetry, the signs of the values alternate:

Complex phases are also possible:

## Neat Examples(1)

Plot random orbits of components of an array with symmetric blocks:

Take an array of depth 6 having 2 symmetric blocks of 3 levels:

Random orbits of the array, after flattening it to a matrix: