On Jul 25, 12:10 am, David Loeffler <[email protected]> wrote: > The hard question is to compute a defining > polynomial for the splitting field of f, identify all the roots of f > as elements of that field, and determine each element of the Galois > group in terms of how it acts on a single generator of the splitting > field.
That's one way of realizing the galois group "concretely". However, the normal way would be to determine *a* splitting field, as a subfield of C or Qp-bar for some good (probably preferably highly split) prime p and present the Galois action as a permutation on these (approximate) roots. That's not nearly as expensive as computing a splitting field as an algebraic extension. In fact, it's mostly a side- effect of the computations you have to do to determine the galois group "abstractly" to begin with. -- -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
