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1 Introduction

Sections

  1. Authors and Acknowledgements
  2. Change history

The GAP 4 package ANUPQ provides an interface to the ANU pq C progam written by Eamonn O'Brien, making the functionality of the C program available to GAP. Henceforth, we shall refer to the ANUPQ package when referring to the GAP interface, and to the ANU pq program or just pq when referring to that C program.

The pq program consists of implementations of the following algorithms:

  1. A p-quotient algorithm to compute pc-presentations for p-factor groups of finitely presented groups.

  2. A p-group generation algorithm to generate pc presentations of groups of prime power order.

  3. A standard presentation algorithm used to compute a canonical pc-presentation of a p-group.

  4. An algorithm which can be used to compute the automorphism group of a p-group.

  5. This part of the pq program is not accessible through the ANUPQ package. Instead, users are advised to consider the GAP 4 package AutPGrp by Bettina Eick and Eamonn O'Brien, which implements a better algorithm in GAP for the computation of automorphism groups of p-groups.

The manual of the ANUPQ package has been written for GAP 4.3. The current version requires GAP 4.3 updated to (at least) fix4. References to GAP 4.2 remain, since the previous version was GAP 4.2 compatible. (See Change history for more details.)

How to read this manual

It is not expected that readers of this manual will read it in a linear fashion from cover to cover; some sections contain material that is far too technical to be absorbed on a first reading.

Firstly, installers of the ANUPQ package will need to read Chapter Installing the ANUPQ package, if they have not already gleaned these details from the README file.

Once the ANUPQ package is installed, users of the ANUPQ package will benefit most by first reading Chapter Mathematical Background and Terminology, which gives a brief description of the background and terminology used (this chapter also cites a number of references for further reading), and the introduction of Chapter Infrastructure (skip the remainder of the chapter on a first reading).

Then the user/reader should pursue Chapter Non-interactive ANUPQ functions in detail, delving into Chapter ANUPQ Options as necessary for the options of the functions that are described. The user will become best acquainted with the ANUPQ package by trying the examples. This chapter describes the non-interactive functions of the ANUPQ package, i.e. ``one-shot'' functions that invoke the pq program in such a way that once GAP has got what it needs, the pq is allowed to exit. It is expected that most of the time, users will only need these functions.

Advanced users will want to explore Chapter Interactive ANUPQ functions which describes all the interactive functions of the ANUPQ package; these are functions that extract information via a dialogue with a running pq process. Occasionally, a user needs the ``next step''; the functions provided in this chapter make use of data from previous steps retained by the pq program, thus allowing the user to interact with the pq program like one can when one uses the pq program as a stand-alone (see guide.dvi in the standalone-doc directory).

After having read Chapters Non-interactive ANUPQ functions and Interactive ANUPQ functions, cross-references will have taken the reader into Chapter ANUPQ Options; by this stage, the reader need only read the introduction of Chapter ANUPQ Options.

After the reader has developed some facility with the ANUPQ package, she should explore the examples described in Appendix Examples.

If you run into trouble using the ANUPQ functions, some troubleshooting hints are given in Section Hints and Warnings regarding the use of Options. If you are still using GAP 4.2 you should probably scan this section before you read Chapter Non-interactive ANUPQ functions. If the troubleshooting hints don't help, Section Authors and Acknowledgements below, gives contact details for the authors of the components of the ANUPQ package.

1.1 Authors and Acknowledgements

The C implementation of the ANU pq standalone was developed by

Eamonn O'Brien
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand
email: obrien@math.auckland.ac.nz

The GAP 4 version of this package was adapted from the GAP 3 version by

Werner Nickel
AG 2, Fachbereich Mathematik, TU Darmstadt
Schlossgartenstr. 7, 64289 Darmstadt, Germany
email: nickel@mathematik.tu-darmstadt.de

An interactive interface using iostreams was developed with the assistance of Werner Nickel by

Greg Gamble
Lehrstuhl D für Mathematik, RWTH Aachen
Templergraben 64, 52062 Aachen, Germany

email: gregg@math.rwth-aachen.de

The authors would like to thank Joachim Neubüser for his careful proof-reading and advice, and for formulating Chapter Mathematical Background and Terminology.

We would also like to thank Bettina Eick who by her testing and provision of examples helped us to eliminate a number of bugs and who provided a number of valuable suggestions for extensions of the package beyond the GAP 3 capabilities.

If you find a bug, the last section of ANUPQ's README describes the information we need and where to send us a bug report; please take the time to read this (i.e. help us to help you).

1.2 Change history

Below we list the main changes between versions of the ANUPQ package.

2.0
Changes to pq program (now version 1.6) and GAP code to fix bug reported by Boris Girnat (thanks Boris!) where too many descendants were generated for a group of class more than 1 with insoluble automorphism group. Also more changes for GAP 4.4, for which

For GAP 4.3fix4, the previous behaviour for the display/suppression and Info-ing of the banner is unchanged, and RequirePackage must be used rather than the new command LoadPackage.

PqSupplementInnerAutomorphisms now returns a record analogous to the AutomorphismGroupPGroup function of the AutPGrp package, and AutomorphismGroupPGroup rather than PqSupplementInnerAutomorphisms is now used to generate the required automorphism group data in descendant calculations. The corresponding PqExample example has similarly been modified.

1.5
Fixed bug in the filtering of ones from input to pq program (thanks to Robert Morse again for the fix). Some preparatory changes made for GAP 4.4.

1.4
Removed an unnecessary file and line from a file in the src directory.

1.3
Efficiency improvements: in particular, the use of IsSyllableWordsFamily as first argument of some FreeGroup commands.

1.2
Fixed some inefficiencies in transmission of relators to the pq program (thanks to Robert Morse for identifying the problem). Updated for bugfixes in fix4 of GAP 4.3, which required some usages of Pcgs to be replaced by GeneralizedPcgs. Requires at least GAP 4.3fix4 and an updated AutPGrp package that uses SetGeneralizedPcgs in lieu of SetPcgs in its definition of ConvertHybridAutGroup.

1.1
First GAP 4 release. Requires at least GAP 4.2, but GAP 4.3 recommended. Supersedes the earlier GAP 3 version (1.0) in many ways; in particular, it provides an interactive interface using the IOStream technology introduced in GAP 4.2.

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ANUPQ manual
March 2004