SymmetrizedDependentComponents
gives the list of components that are equivalent to the component comp by the symmetry sym.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (2)Survey of the scope of standard use cases
This is an array with symmetry:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-lrvv65

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

https://wolfram.com/xid/0bsvv2e84zk9k84poz-gyyzdf

The respective values coincide by symmetry:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-39qugz

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

https://wolfram.com/xid/0bsvv2e84zk9k84poz-dvdfi0

Properties & Relations (4)Properties of the function, and connections to other functions
Using Symmetric, SymmetrizedDependentComponents is essentially equivalent to Permutations:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-teleit

SymmetrizedDependentComponents allows permuting only some elements:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-vjhn3v

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

https://wolfram.com/xid/0bsvv2e84zk9k84poz-2jhdes

https://wolfram.com/xid/0bsvv2e84zk9k84poz-0vvh6r


https://wolfram.com/xid/0bsvv2e84zk9k84poz-bmq246

Take a symmetry for a depth-4 array:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-2stpkk
There are 55 independent components in dimension 5:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-4mdeqz

Compute the respective dependent components and flatten the result:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-fyzeh4

The remaining components are all zero by symmetry:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-z4b041

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:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-v06777


https://wolfram.com/xid/0bsvv2e84zk9k84poz-ox2km7


https://wolfram.com/xid/0bsvv2e84zk9k84poz-zy4my6


https://wolfram.com/xid/0bsvv2e84zk9k84poz-62w0br

Complex phases are also possible:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-m3l560


https://wolfram.com/xid/0bsvv2e84zk9k84poz-z3m7r3


https://wolfram.com/xid/0bsvv2e84zk9k84poz-yylm91


https://wolfram.com/xid/0bsvv2e84zk9k84poz-2fb56b

Neat Examples (1)Surprising or curious use cases
Plot random orbits of components of an array with symmetric blocks:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-x2uxgv

https://wolfram.com/xid/0bsvv2e84zk9k84poz-ffibpo
Take an array of depth 6 having 2 symmetric blocks of 3 levels:

https://wolfram.com/xid/0bsvv2e84zk9k84poz-gd9ppf

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

https://wolfram.com/xid/0bsvv2e84zk9k84poz-84wba9

Wolfram Research (2012), SymmetrizedDependentComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html.
Text
Wolfram Research (2012), SymmetrizedDependentComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html.
Wolfram Research (2012), SymmetrizedDependentComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html.
CMS
Wolfram Language. 2012. "SymmetrizedDependentComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html.
Wolfram Language. 2012. "SymmetrizedDependentComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html.
APA
Wolfram Language. (2012). SymmetrizedDependentComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html
Wolfram Language. (2012). SymmetrizedDependentComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html
BibTeX
@misc{reference.wolfram_2025_symmetrizeddependentcomponents, author="Wolfram Research", title="{SymmetrizedDependentComponents}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html}", note=[Accessed: 29-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_symmetrizeddependentcomponents, organization={Wolfram Research}, title={SymmetrizedDependentComponents}, year={2012}, url={https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html}, note=[Accessed: 29-May-2025
]}