> < ^ From:

^ Subject:

Dear GAP-Forum,

due to an error for which I unfortunately cannot blame a computer,

part of the new documentation for GAP 3.4 has not been included in the

release (while the corresponding code is included). This documentation covers:

o The library of transitive groups,

o Generic algebraic extensions of fields and

o Computation of (isomorphism types) of Galois groups.

This documentation will be included in the next patch, that is to be

released in the near future.

I apologize for this mistake. If anyone is in urgent need of the

documentation, I can provide him the corresponding files already now.

Alexander Hulpke (Alexander.Hulpke@math.rwth-aachen.de)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In short, the new commands include:

TransitiveGroup(deg,nr);

Creates a transitive permutation group of the isomorphy type given in

Butler/McKay: the transitive groups of degree up to 11, CommAlg 11(1983),

863--911

TransitiveIdentification(grp);

if grp is a transitive permutation group of degree d<=11, then this command

yields the number of the permutation isomorphy type of grp, i.e.

grp ~= TransitiveGroup(d,TransitiveIdentification(grp)).

if f is a polynomial over the rationals, then

Galois(f);

yields the number of the isomorphism type of the corresponding Galois group.

(This might take substantial time).

ProbabilityShapes(f);

return a list of guesses for the isomorphism type of the Galois group. It is

much faster, but might be wrong.

If f is any polynomial, then

AlgebraicExtension(f);

creates the corresponding algebraic extension,

RootOf(f);

the generating element. The base field is naturally embedded.

Multiple algebraic extensions are not supported.

Polynomial factorization is possible over Algebraic extensions of finite

fields or the rationals (as well as over these ground fields themselves)\

by specifying a polynomial over this field and using 'Factor'.

Polynomial factorization over the rationals has been possible (but

undocumented) already in version 3.3, but this algorithm has been improved

significantly in 3.4.

> < [top]