# cyclotomicField -- cyclotomic field construction

## Synopsis

• Usage:
cyclotomicField (i)
• Inputs:
• i, an integer, the power of the root to be adjoined.
• Outputs:
• S, A cyclotomic field with $1^(1/i)$ adjoined

## Description

 i1 : S = cyclotomicField (5) o1 = S o1 : PolynomialRing i2 : isField S o2 = true i3 : r = S_0 o3 = ww 5 o3 : S i4 : (r^9, r^10, r^11) 3 2 o4 = (- ww - ww - ww - 1, 1, ww ) 5 5 5 5 o4 : Sequence i5 : T = S[x,y] o5 = T o5 : PolynomialRing i6 : I = ideal (x-r) o6 = ideal(x - ww ) 5 o6 : Ideal of T i7 : dim I o7 = 1

## Caveat

Strange things can happen with the reduction of the coefficients. In M2 v <= 1.2 dimension is off by one.