numtheory/iscyclotomic(deprecated) - Help

numtheory

 iscyclotomic
 test if a polynomial is cyclotomic

 Calling Sequence iscyclotomic(m, x) iscyclotomic(m, x, 'n')

Parameters

 m - polynomial in x over the rationals x - name n - (optional) name for the output of the order of the polynomial, if cyclotomic

Description

 • Important: The numtheory[iscyclotomic] command 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](..).

Examples

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $m≔\mathrm{cyclotomic}\left(10,x\right)$
 ${m}{≔}{{x}}^{{4}}{-}{{x}}^{{3}}{+}{{x}}^{{2}}{-}{x}{+}{1}$ (1)
 > $\mathrm{iscyclotomic}\left(m,x,'n'\right)$
 ${\mathrm{true}}$ (2)
 > $n$
 ${10}$ (3)
 > $f≔{x}^{5}+{x}^{4}+{x}^{3}+{x}^{2}+x+1$
 ${f}{≔}{{x}}^{{5}}{+}{{x}}^{{4}}{+}{{x}}^{{3}}{+}{{x}}^{{2}}{+}{x}{+}{1}$ (4)
 > $\mathrm{iscyclotomic}\left(f,x\right)$
 ${\mathrm{false}}$ (5)