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#     Australian National University p-Quotient Program 
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#     Version 1.8
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#     June 2001, February 2002, February 2004, July 2005, January 2006
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This implementation was developed in C by 

Eamonn O'Brien 
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland, New Zealand

E-mail: obrien@math.auckland.ac.nz

WWW http://www.math.auckland.ac.nz/~obrien

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The program provides access to implementations of the following algorithms:

1. A p-quotient algorithm to compute a power-commutator presentation
for a p-group.  The algorithm implemented here is based on that 
described in Newman and O'Brien (1996), Havas and Newman (1980),
and papers referred to there.

Another description of the algorithm appears in Vaughan-Lee (1990b).
A FORTRAN implementation of this algorithm was programmed by 
Alford & Havas. The basic data structures of that implementation 
are retained.

The current implementation incorporates the following features:

a. collection from the left (see Vaughan-Lee, 1990b); 
   Vaughan-Lee's implementation of this collection 
   algorithm is used in the program;

b. an improved consistency algorithm (see Vaughan-Lee, 1982);

c. new exponent law enforcement and power routines; 

d. closing of relations under the action of automorphisms;

e. some formula evaluation.

2. A p-group generation algorithm to generate descriptions of p-groups. 
The algorithm implemented here is based on the algorithms described in 
Newman (1977) and O'Brien (1990). A FORTRAN implementation of this 
algorithm was earlier developed by Newman & O'Brien.  

3. A standard presentation algorithm used to compute a canonical 
power-commutator presentation of a p-group. The algorithm 
implemented here is described in O'Brien (1994).

4. An algorithm which can be used to compute the automorphism group of 
a p-group. The algorithm implemented here is described in O'Brien (1995).


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Access to parts of this program is provided via GAP, Magma, and Quotpic.

This program is supplied as a package within GAP, both GAP 3.4 and  GAP4.
The link from GAP to pq is described in the manual for GAP  3.4,  and  is
described in a separate manual supplied with the ANUPQ package  anupq.zoo
archive for GAP4.

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#References
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George Havas and M.F. Newman (1980), "Application of computers
to questions like those of Burnside", Burnside Groups (Bielefeld, 1977), 
Lecture Notes in Math. 806, pp. 211-230. Springer-Verlag.

M.F. Newman and E.A. O'Brien (1996), "Application of computers to 
questions like those of Burnside II", 
Internat. J. Algebra Comput. 6, 593-605.

M.F. Newman (1977), "Determination of groups of prime-power order", 
Group Theory (Canberra, 1975). Lecture Notes in Math. 573, pp. 73-84. 
Springer-Verlag.

E.A. O'Brien (1990), "The p-group generation algorithm",
J. Symbolic Comput. 9, 677-698.

E.A. O'Brien (1994), ``Isomorphism testing for p-groups", 
J. Symbolic Comput. 17, 133-147.

E.A. O'Brien (1995), ``Computing automorphism groups of p-groups", 
Computational Algebra and Number Theory, (Sydney, 1992), pp. 83--90. 
Kluwer Academic Publishers, Dordrecht.

M.R. Vaughan-Lee (1982), "An Aspect of the Nilpotent Quotient Algorithm", 
Computational Group Theory (Durham, 1982), pp. 76-83. Academic Press.

Michael Vaughan-Lee (1990a), The Restricted Burnside Problem,
London Mathematical Society monographs (New Ser.) #5.
Clarendon Press, New York, Oxford.

M.R. Vaughan-Lee (1990b), "Collection from the left", 
J. Symbolic Comput. 9, 725-733.

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1. For installation for use with GAP4 please go to the README in the
   main directory. The directory mapping of the anupq directory derived
   from anupq.zoo is as follows:

   doc -- manual for the GAP4 package that interfaces with pq
   standalone-doc -- documentation on use of the pq standalone program
   standalone -- contains the pq standalone TEST, examples, isom directories
   include  -- C header files 
   src -- C source files and a Makefile
   lib -- GAP library files
   tst -- GAP test files
   examples -- GAP examples

   After doing `make restoredirs' in the anupq directory, the anupq sub-
   directories are remapped to the way they are in the distribution found at:

   http://www.math.auckland.ac.nz/~obrien

   namely the GAP4 doc directory, main directory README and a number of
   other files there are moved to the directory doc; standalone-doc
   is renamed doc; the examples, lib and tst directories are moved into
   the gap directory; the examples, isom and TEST subdirectories of
   standalone are moved to be in the main directory; and this README is 
   moved to be in the main directory.

   Doing `make GAP4remapdirs' establishes the directory structure above.

2. The file, guide.tex, in the standalone-doc (or doc) directory is a 
   LaTeX file. It is a basic guide to the use of the p-Quotient Program. 

3. By default, the program has the following limits:
   the maximum number of pc generators is 2^16 - 1 = 65535; 
   the maximum number of defining generators is 2^9 - 1 = 511; 
   the maximum class is 2^6 - 1 = 63. 

   The data structures require that the following holds:
   the sums of the exponents of 2 from  the above three quantities 
   is at most (the number of bytes in a word) - 1.
   Hence the sum is usually 31.

   The program can be compiled in two modes; in fixed mode
   the above limits are enforced; in runtime mode, these are 
   also the default; however, the limit on the number of defining 
   generators and the class can be altered by the user via 
   on-line options "-c" and "-d"; if such selections are made, 
   the maximum number of pc generators is consequently altered; 
   a user must decide the limit on *each* of the number of 
   defining generators and the class.

   The default limits are set in the header files:
   storage_fixed.h (for fixed version)
   runtime.h       (for runtime version)

   On average, the fixed mode version performs 5-10% more 
   efficiently than the runtime version.

   If you wish to compile the runtime mode version, then set
   -DRUN_TIME as a compiler flag in the Makefile.

4. The README in the main directory explains how to install the
   GAP4 package ANUPQ together with the pq binary.

   *Otherwise*, to create the pq binary --
   a. change to the src directory;
   b. ensure that the conditional compilation flags in the 
      Makefile are set correctly; the -DLARGE_INT flag controls
      the storage and display of automorphism group orders;
      if you want to use this flag, you must have an up-to-date 
      copy of the GNU MP procedures on your machine;
   c. system dependent features are collected in system.c;
      in particular, you may wish to look at the run time function 
      to ensure that the CPU time reported by the program is correct;
   d. type make pq
   e. to remove all of the object files, type make clean

   A binary file, pq, will be placed in a subdirectory of bin which
   is created when configure and make are run in the main directory.

5. The total space requirements for this directory (including 
   the binary but excluding the object files) is about 3 MB.

6. In p-group generation, if the automorphism group of the 
   starting group is insoluble, then pq calls one of 
   GAP or Magma to perform particular stabiliser computations 
   (see the User Guide for more details).
   The user of pq may choose which of these systems is to 
   be called --  however, the choice for this link MUST be 
   made by the user at compilation time by setting one of the
   GAP_LINK or Magma_LINK flags in the Makefile.
   Points 7 and 8 below discuss each of these links in turn.
   
7. The magma directory contains a cshell file, Magma_script, and 
   one Magma library file, stabcalc.m 
   
   If you plan to use the link from this program to the system Magma, 
   you will need to take the following action:

   a. An environment variable, Magma_DIR, must be set to have as its
      value the path to the directory cayley. If you wish to alter
      the name of this environment variable, edit the occurrence
      of this variable in the src file Magma.c, its occurrence
      in Magma_script, and remake the binary.

   b. The cshell file, Magma_script, executes magma. 
      The binary for magma must be in your path.

   The "egrep -v" commands in the Magma_script file are used to
   remove certain output which occurs in the Magma log file.
   In order that the Magma_output file is processed correctly
   by pq, it is necessary that no text occurs before the listing 
   of two integers and the generators of the stabiliser. 
   On certain machines, the output file Magma_output may contain 
   other junk before these entries -- if such is the case on your 
   machine, you will need to add additional "egrep -v" command to 
   remove such material.

8. The link from pq to GAP assumes that you use GAP 3.4 or GAP4
   *with* the *ANUPQ package* installed.

   If the binary for GAP 3.4 or GAP4 is called gap and is in your 
   default path, you need do no more; if it is not in your path, 
   you must set an environment variable ANUPQ_EXEC_GAP to 
   point to the GAP executable.

9. The TEST subdirectory of standalone contains a number of log files, 
   with extension .orig, together with a cshell file called TEST.
   This test program runs through a number of the examples 
   in the examples directory and compares the results generated with 
   those listed in the .orig files of this directory. If the 
   p-quotient program is running correctly, the TEST program 
   should report only differences in the date, name of machines 
   and times taken. If there are other significant differences, 
   please report.
   
   Execute the test program by typing TEST 
   (If your pq directory structure is different, you may need to alter 
   the relative paths in TEST for both binary and command files.)

   The total time taken for the test on a SPARCstation 10/51 is
   about 30 seconds of user time.

10. See the documentation for information on run-time parameters.

11. Please report bugs/problems/feedback to obrien@math.auckland.ac.nz
