cyclo.spad line 1 [edit on github]

Author: W. Hebisch References: A. Arnold, M. Monagan, Calculating cyclotomic polynomials, Math. Comp. 80 (276) 2011, 2359-2379.

cocyclotomic_decomposition: Integer -> List SparseUnivariatePolynomial Integer

cocyclotomic_decomposition(n) computes list of irreducible factors of x^n + 1 over integers.

cyclotomic?: SparseUnivariatePolynomial Integer -> Union(Integer, failed)

cyclotomic?(p) checks if p is a cyclotomic polynomial. If yes returns n such that p = cyclotomic(n). Otherwise returns “failed”.

cyclotomic: Integer -> SparseUnivariatePolynomial Integer

cyclotomic(n) computes n-th cyclotomic polynomial.

cyclotomic_array: Integer -> PrimitiveArray Integer

cyclotomic_array(n) computes pa containing lower half of coefficients of n-th cyclotomic polynomial. maximal index in pa is eulerPhi(n)/2. Due to symmetry this is enough to reconstruct cyclotomic polynomial from computed coefficients.

cyclotomic_decomposition: Integer -> List SparseUnivariatePolynomial Integer

cyclotomic_decomposition(n) computes list of irreducible factors of x^n - 1 over integers.

inverse_cyclotomic: Integer -> SparseUnivariatePolynomial Integer

inverse_cyclotomic(n) computes n-th inverse cyclotomic polynomial, that is (x^n - 1)/cyclotomic(n).