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# cyclotomicField -- cyclotomic field construction

- 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.

## See also

- cyclotomicPoly -- Cyclotomic Polynomial

## For the programmer

The object cyclotomicField is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Cyclotomic.m2:176:0.