GeneralizedPower [f,x,k]
GeneralizedPower
GeneralizedPower [f,x,k]
Details
- GeneralizedPower is used to represent an integer power of a binary operation.
- If f has the Flat attribute, GeneralizedPower [f,x,k] is equivalent to f[].
- GeneralizedPower [f,x,k] is typeset as .
Examples
open all close allBasic Examples (1)
Represent the third power of NonCommutativeMultiply at x+y:
GeneralizedPower[NonCommutativeMultiply, x + y, 3]Use NonCommutativeExpand to expand the power of sum:
NonCommutativeExpand[%, NonCommutativeAlgebra[]]The third GeneralizedPower is equivalent to applying the operation to three copies of the argument:
NonCommutativeExpand[(x + y)**(x + y)**(x + y), NonCommutativeAlgebra[]]Scope (5)
Power of a symbolic operation f:
GeneralizedPower[f, g[x, y], 3]Expand the power over an algebra with product f and vector space addition g:
NonCommutativeExpand[%, NonCommutativeAlgebra[<|"Multiplication" -> f, "Addition" -> g|>]]GeneralizedPower of Plus and Times autosimplify:
GeneralizedPower[Plus, x, k]GeneralizedPower[Times, x, k]Small positive integer GeneralizedPower of numeric functions evaluates at number arguments:
GeneralizedPower[Power, 2, 7]Fold[Power, Table[2, 7]]Powers of operations with built-in symbols:
GeneralizedPower[Composition, f, k]GeneralizedPower[Dot, a, k]GeneralizedPower[CircleTimes, a, k]Autosimplification of GeneralizedPower :
f[GeneralizedPower[f, x, k], x]More general autosimplification for associative (Flat ) operations:
SetAttributes[g, Flat]g[a, x, GeneralizedPower[g, x, k], x, GeneralizedPower[g, x, m], x, b]GeneralizedPower[g, GeneralizedPower[g, x, k], m]Properties & Relations (2)
GeneralizedPower of Times is Power :
GeneralizedPower[Times, x, k]GeneralizedPower of Plus is Times :
GeneralizedPower[Plus, x, k]Related Guides
History
Text
Wolfram Research (2025), GeneralizedPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneralizedPower.html.
CMS
Wolfram Language. 2025. "GeneralizedPower." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeneralizedPower.html.
APA
Wolfram Language. (2025). GeneralizedPower. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeneralizedPower.html
BibTeX
@misc{reference.wolfram_2026_generalizedpower, author="Wolfram Research", title="{GeneralizedPower}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/GeneralizedPower.html}", note=[Accessed: 03-July-2026]}
BibLaTeX
@online{reference.wolfram_2026_generalizedpower, organization={Wolfram Research}, title={GeneralizedPower}, year={2025}, url={https://reference.wolfram.com/language/ref/GeneralizedPower.html}, note=[Accessed: 03-July-2026]}