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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)

Stefan

Miles-Receive-Header: reply

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