joinCyclotomic -- Join ideals in polynomial rings over different cyclotomic fields

i1 : F = cyclotomicField 3; G = cyclotomicField 4;

i3 : R = F[t]; I = ideal (t-F_0^2)

o4 = ideal(t + ww  + 1)
                 3

o4 : Ideal of R

i5 : S = G[t]; J = ideal (t^2-G_0)

            2
o6 = ideal(t  - ww )
                  4

o6 : Ideal of S

i7 : joinCyclotomic {I,J}

                  2           2     3
o7 = {ideal(t + ww  ), ideal(t  - ww  )}
                  12                12

o7 : List