Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[IsCyclotomicPolynomial] instead.

The iscyclotomic(m, x) calling sequence returns true if m(x) is a cyclotomic polynomial, and false otherwise.

The iscyclotomic(m, x, 'n') calling sequence also assigns the order of the cyclotomic polynomial to n when the function returns true.

This function is part of the numtheory package, and so can be used in the form iscyclotomic(..) only after executing the command with(numtheory) or with(numtheory,iscyclotomic). The function can always be accessed in the long form numtheory[iscyclotomic](..).

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$m≔\mathrm{cyclotomic}\left(10\,x\right)$

$m≔x^4-x^3+x^2-x+1$

$\mathrm{iscyclotomic}\left(m\,x\,'n'\right)$

$\mathrm{true}$

$n$

$10$

$f≔x^5+x^4+x^3+x^2+x+1$

$f≔x^5+x^4+x^3+x^2+x+1$

$\mathrm{iscyclotomic}\left(f\,x\right)$

$\mathrm{false}$