Cyclotomic

Cyclotomic(n, x)

returns the Cyclotomic polynomial C_n(x).

See:

• Wikipedia - Cyclotomic polynomial

Examples

>> Cyclotomic(25,x)
1+x^5+x^10+x^15+x^20

The case of the 105-th cyclotomic polynomial is interesting because 105 is the lowest integer that is the product of three distinct odd prime numbers and this polynomial is the first one that has a coefficient other than 1, 0 or −1:

>> Cyclotomic(105, x)
1+x+x^2-x^5-x^6-2*x^7-x^8-x^9+x^12+x^13+x^14+x^15+x^16+x^17-x^20-x^22-x^24-x^26-x^28+x^31+x^32+x^33+x^34+x^35+x^36-x^39-x^40-2*x^41-x^42-x^43+x^46+x^47+x^48

Implementation status

• ✅ - full supported

Github

• Implementation of Cyclotomic