The GAP 4 package `GaloisGroups'

This package implements the computation of Galois group.

For arithmetic computations, the package relies on PARI/GP called via the PARIInterface package.

Requirements

GaloisGroups depends on other Galois packages

• GAPDoc
• Digraphs
• ferret
• alnuth
• TransGrp
• PARIInterface

as well as the development version of PARI/GP (see Installation below)

Installation

For the moment you need to use the development version of pari that implement function unavailable in PARI/GP 2.11 (e.g. ZpXQX_liftroots). If you need the compiler to know about a special location of PARI/GP runs configure with appropriate options

$ ./configure [GAPPATH] --with-pari [PARIPATH]

Documentation

Full information and documentation can be found in the manual, available as PDF doc/manual.pdf or as HTML doc/chap0_mj.html, or on the package homepage at

https://gap-packages.github.io/GaloisGroups/

Bug reports and feature requests

Please submit bug reports and feature requests via our GitHub issue tracker:

https://github.com/gap-packages/GaloisGroups/issues

License

GaloisGroups is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

For details see the files COPYRIGHT.md and LICENSE.

Testing

Tests are implemented in tst/. To run them do

$ {GAP} tst/testall.g

References

• C. Fieker, J. Klüners "Computation of Galois groups of rational polynomials" (2014)
• A. Hulpke "Galois groups through invariant relations" (1999)
• A. Hulpke "Finding intermediate subgroups" (2017)