Leonard Soicher writes:
Given generators a,b,c,... of a finite algebraic extension of the
rationals, would it not be possible for Gap 3.4+epsilon to calculate a
minimal polynomial for a single element t such that
Q(t)=Q(a,b,c,...), by applying an algorithmic version of the primitive
element theorem? It seems like most of what is necessary is already
in Gap 3.4.
Yes, that should be possible, and it can be done completely in the GAP
language. If somebody wants urgently to have such a function, and is
willing to write it, we would welcome if he deposits it in 'incoming'
directory on our server.
We have plans to provide facilities for handling general field
extensions, but then we would like to try to do this in a reasonably
organized package rather than by providing a collection of
patches. This however will take its time, i.e. epsilon is likely to be
a positive integer.
Kind regards Joachim Neubueser