SymmetrizedDependentComponents
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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_2024_symmetrizeddependentcomponents, author="Wolfram Research", title="{SymmetrizedDependentComponents}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html}", note=[Accessed: 07-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_symmetrizeddependentcomponents, organization={Wolfram Research}, title={SymmetrizedDependentComponents}, year={2012}, url={https://reference.wolfram.com/language/ref/SymmetrizedDependentComponents.html}, note=[Accessed: 07-January-2025
]}