[GAP Forum] Transitive groups up to degree 15.

2017-08-04 Thread Mark Leaver
Hi,

https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/gal15.pdf

It's been about 20 years since the publication of this paper by Kluners and 
Malle and in it they provide a method of determining certain transitive groups
of up to degree 15 using the rigidity method for simple groups (as one can see 
in the tables provided at the end).

Furthermore, they additionally provide explicit constructions of polynomials 
over Q with regards to the transitive subgroups.

They mention on page 14 that this was achieved by GAP.

My question is twofold:

1) Since it has been 20 years and methods may have changed, is anyone aware of 
the quickest implementation (an avaiable script) of the rigidity method 
(section 2.1.1) as mentioned in GAP in order to realize transitive groups
up to degree 15 (or higher if it is possible) as Galois groups over Q?

2)Additionally, they state a list of varying algorithms in order to determine 
the polynomials of the associated transitive groups. Is there a standard
implementation/script available on GAP nowadays for this in having some 
transitive group of a similar degree (as they've done) and obtain some 
polynomial realized over Q.

Many thanks,

Mark
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[GAP Forum] Transitive groups up to degree 15.

2017-08-04 Thread Mark Leaver
Hi,

https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/gal15.pdf

It's been about 20 years since the publication of this paper by Kluners and 
Malle and in it they provide a method of determining certain transitive groups
of up to degree 15 using the rigidity method for simple groups (as one can see 
in the tables provided at the end).

Furthermore, they additionally provide explicit constructions of polynomials 
over Q with regards to the transitive subgroups.

They mention on page 14 that this was achieved by GAP.

My question is twofold:

1) Since it has been 20 years and methods may have changed, is anyone aware of 
the quickest implementation (an avaiable script) of the rigidity method 
(section 2.1.1) as mentioned in GAP in order to realize transitive groups
up to degree 15 (or higher if it is possible).

2)Additionally, they state a list of varying algorithms in order to determine 
the polynomials of the associated Galois groups. Is there a standard
implementation/script available on GAP for this in having some transitive group 
of a similar degree (as they've done) and obtain some polynomial to be realized 
over Q.

Many thanks,

Mark

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