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

See also

• cyclotomicPoly -- Cyclotomic Polynomial