This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# Cyclotomic

 Cyclotomicgives the n 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 roots of :
 Out[1]=
The roots are the irreducible 5 roots of :
 Out[2]=
 Scope   (1)
 Applications   (6)
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 cyclotomic polynomial:
The first cyclotomic polynomial with a coefficient other than 0, ±1:
Nonzero coefficients of successive cyclotomic polynomials:
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