fieldBaseChange -- a function to compute the base change between GaloisFields

Synopsis

• Usage:

  fieldBaseChange(R, K)

• Inputs:
  • R, a ring, with a GaloisField $L$ as its coefficient ring
  • K, a Galois field, extension of $L$
• Outputs:
  • a sequence, ($T$ ,$f$) where $T = R \otimes_L K$ is the base-changed ring, $f:R\to T$ is the ring map $R\otimes_L L\to R\otimes_L K$ induced from $L\to K$.

Description

i1 : R = GF(8)[x,y,z]/(x*y-z^2)

o1 = R

o1 : QuotientRing

i2 : K = GF(64)

o2 = K

o2 : GaloisField

i3 : (T,f) = fieldBaseChange(R,K)

                            5    4    2
o3 = (T, map(T,R,{x, y, z, a  + a  + a  + 1}))

o3 : Sequence

i4 : describe T

      K[x..z]
o4 = --------
            2
     x*y + z

i5 : describe f

                           5    4    2
o5 = map (T, R, {x, y, z, a  + a  + a  + 1})