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gives the n^(th) cyclotomic polynomial in x.
  • The cyclotomic polynomial of order is defined to be , where the product runs over integers less than that are relatively prime to .
The roots are the irreducible 5^(th) roots of :
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The roots are the irreducible 5^(th) roots of :
Click for copyable input
TraditionalForm formatting:
Values of successive cyclotomic polynomials at 1:
Calculate for which the decimal expansion of has a unique period:
Plot cyclotomic polynomials:
Plot arguments of roots of Cyclotomic:
Plot the degree and number of terms of cyclotomic polynomials:
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^(th) cyclotomic polynomial:
The first cyclotomic polynomial with a coefficient other than 0, ±1:
Nonzero coefficients of successive cyclotomic polynomials:
New in 1