[GAP Forum] RCWA 2.5

[Stefan Kohl]

Dear Forum,

This is to announce the release of RCWA 2.5.

Given disjoint residue classes r1(m1) and r2(m2) of the integers, let the
corresponding class transposition be the permutation of Z which interchanges
r1 + km1 and r2 + km2 for each integer k and which fixes all other points.
Further let CT(Z) be the group which is generated by the set of all class
transpositions of Z. This group is simple.

The RCWA package permits to compute with subgroups of CT(Z).

The class of finitely generated subgroups of CT(Z) includes for example

  - finite groups,
  - free groups of finite rank,
  - free products of finite groups,
  - divisible torsion groups,
  - groups which do not have finite presentations, and
  - groups whose membership problem is algorithmically unsolvable.

This class of groups is closed under taking direct products and under taking
wreath products with finite groups and with the infinite cyclic group (Z,+).

The main changes since the last announced version RCWA 2.2
of September / October 2006 are:

  - The manual has undergone a revision.

  - Iterators for infinite groups have been implemented.

  - Orbit objects representing possibly infinite orbits have been introduced.

  - There are new operations
     - `EpimorphismFromFpGroup' and
     - `PartitionsIntoResidueClasses',
    the groups CT(R) are now available as GAP objects, and there are
    a couple of new functions, attributes and properties.

  - There are new methods available for various operations, and various
    existing methods have been improved --
    Among others, the membership test has been improved, and the case that
    the underlying ring is a polynomial ring GF(q)[x] is now supported better.

  - Some functionality for monoids has been added --
    see the short new manual chapter "Residue-Class-Wise Affine Monoids".

  - Graphics functions `SaveAsBitmapPicture', `ReadFromBitmapPicture'
    and `DrawOrbitPicture' have been added.
    Examples of pictures generated with `DrawOrbitPicture' can be found at
    http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/rcwa/pictures.html .

  - Now there is a new preprint available, which describes a significant part
    of the algorithms and methods implemented in this package in detail.

  - A copy of my thesis is distributed with the package again, since a user
    suggested me to do so.

  - The source code has been restructured and commented better in many places.

As usual, RCWA is available at

     http://www.gap-system.org/Packages/rcwa.html .

It remains to say that I would very much appreciate any comments,
bug reports, hints and of course reports about results found with
the help of RCWA.

Wishing you fun and success using this package,

     Stefan Kohl