Built-in Mathematica Symbol

Cyclotomic

Cyclotomic[n, x]
gives the n

cyclotomic polynomial in

.

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 -1:

The roots are the irreducible 5

roots of -1:

Values of successive cyclotomic polynomials at 1:

Calculate unique primes 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: