Dear Gap - Forum,
> Is there a chance of speeding up Galois() for GAP4?
One reason of not having converted the existing code is that I plan to
implement some improvements that should increase speed as well as extend the
algorithm to higher degrees, but as the code does not yet exist I don't want
to promise anything yet.
Would it be in principle possible to give a valid algorithm for galois group
computation for arbitrary degrees, and if so, is there anything which could
be stated about its complexity ? If not : is it possible to prove this ?
This might perhaps require a general algorithm for the construction of the
transitive permutation groups of a given degree - does such an algorithm
exist, or are all approaches in this direction only 'semi - automated' /
only valid for 'small' degrees ?
(For the theory, construction of all non - isomorphic permutation groups of a
given degree is certainly no problem -- the computability comes just from the fact
that there is nothing infinite to be taken into consideration; this certainly
gives no practical algorithm)