Cyclotomic[n,x]
gives the n cyclotomic polynomial in x.


Cyclotomic
Cyclotomic[n,x]
gives the n cyclotomic polynomial in x.
Examples
open all close allScope (1)
TraditionalForm formatting:
Applications (6)
Values of successive cyclotomic polynomials at 1:
Calculate unique primes for which the decimal expansion of has a unique period:
Plot arguments of roots of Cyclotomic:
Plot the degree and number of terms of cyclotomic polynomials:
Properties & Relations (7)
Factor a cyclotomic polynomial over an extension field:
Generate cyclotomic polynomials from a definition:
Use an alternative definition, valid for :
Form products of cyclotomic polynomials:
Plot the Riemann surface of an inverse of a cyclotomic polynomial over the complex plane:
Plot the complex roots of successive derivatives of the 50 cyclotomic polynomial:
See Also
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), Cyclotomic, Wolfram Language function, https://reference.wolfram.com/language/ref/Cyclotomic.html.
CMS
Wolfram Language. 1988. "Cyclotomic." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Cyclotomic.html.
APA
Wolfram Language. (1988). Cyclotomic. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cyclotomic.html
BibTeX
@misc{reference.wolfram_2025_cyclotomic, author="Wolfram Research", title="{Cyclotomic}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Cyclotomic.html}", note=[Accessed: 06-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_cyclotomic, organization={Wolfram Research}, title={Cyclotomic}, year={1988}, url={https://reference.wolfram.com/language/ref/Cyclotomic.html}, note=[Accessed: 06-August-2025]}