Galois group of the splitting field K of x^4+2 over Q.
#1 Find field generators of K over Q.
#2, #3 Find degree of K over Q, and Gal(K/Q)
#3 continued find action of G on the field generators from #1
#3 continued find action of G on roots of x^4+2
#3 concluded, #4 lattice of subgroups of G
#4 continued find fixed field of each subgroup of G
#4 continued find lattice of subfields corresponding to latttice of subgroups
#5 find normal subgroups of G and corresponding Galois extensions of Q
#6 find primitive element of K over Q
