This file offers 6 functions: InversePhiBound
, gcdList
, cyclotomic
, IsCyclotomicGraeffe
, IsCyclotomicIter
, and IsCyclotomic
.
Let f
be two RingElem
values representing univariate polynomials in a polynomial ring P
over ZZ
or QQ
.
Let n
be a positive integer.
InversePhiBound(n)
-- returns a BigInt
representing an upper bound for the inverse EulerTotient
of n
- using OEIS sequence A355667.
gcdList(L)
-- returns a RingElem
, namely the gcd
of a vector of RingElem
s.
cyclotomic(P, K)
-- returns a RingElem
representing the K
-th cyclotomic polynomial in the ring P
.
IsCyclotomicGraeffe(f)
-- returns an unsigned long n
indicating that f
is the n
-th cyclotomic polynomial - using a Graeffe transformation approach.
IsCyclotomicIter(f)
-- returns an unsigned long n
indicating that f
is the n
-th cyclotomic polynomial - using an iterative approach.
IsCyclotomic(f)
-- returns an unsigned long n
indicating that f
is the n
-th cyclotomic polynomial - choosing an approach from the above.
n
-th cyclotomic polynomial is always +1 if n > 1
.
rev(f) == f
?
UnivariateIndetIndex
still returns the index of the variable.
2022