1 Introduction
  
  
  1.1 Introduction to the HAPprime package
  
  HAPprime    is   a   package   for   the   GAP   computer   algebra   system
  (http://www.gap-system.org/), and which extends the HAP `Homological Algebra
  Progamming'        package        written        by       Graham       Ellis
  (http://hamilton.nuigalway.ie/Hap/www/).  It  provides  algorithms  and data
  structures  for calculating cohomology ring presentations and resolutions of
  small  prime-power  groups. As well as new functions, HAPprime also provides
  some  equivalents  for  some  existing  HAP  functions  that  are  much more
  memory-efficient and occasionally faster.
  
  In particular, the main reasons you may want to use HAPprime are
  
  --    the  calculation of resolutions of prime-power groups in HAPprime uses
        significantly  less  memory  than  the  equivalent  function  in  HAP,
        allowing  resolutions  (and  cohomology  ring presentations) of larger
        groups to be calculated (see Section 2.3);
  
  --    HAPprime  can  compute  polynomial  ring  presentations for cohomology
        rings calculated using either HAP or HAPprime (see Section 2.2-1);
  
  --    we provide a method which ensures that complete and correct cohomology
        rings are computed. This is a an implementation of Len Evens' original
        proof  of the finite presentation of the cohomology rings (see Section
        2.2-2).
  
  
  1.2 Required software
  
  The  HAPprime  package  requires  GAP version 4.4 or greater and HAP version
  1.8.9  or  greater.  For  calculating provably-correct cohomology rings, the
  Singular commutative algebra system (http://www.singular.uni-kl.de/) and the
  singular GAP package are also required.
  
  
  1.3 Installing HAPprime
  
  To  install  the  HAPprime  Package,  unpack  the archive file into your GAP
  packages  directory  (either  usually  the  pkg  directory  of  your  GAP  4
  installation  if you have access to it, or some local pkg directory that GAP
  can find). The HAPprime files will all be installed in a subdirectory called
  happrime-0.3.2.
  
  
  1.4 Loading and testing HAPprime
  
  The  HAPprime  package is not loaded by default when GAP is started. To load
  the package, type the following at the GAP prompt:
  
  ---------------------------  Example  ----------------------------
    gap> LoadPackage( "HAPprime");
  ------------------------------------------------------------------
  
  If HAPprime isn't already in memory, it is loaded and the author information
  is  displayed.  If  you  are a frequent user of HAPprime, you might consider
  putting this line in your .gaprc file.
  
  The correct installation of HAPprime can be tested by using the test routine
  tst/testall.g:
  
  ---------------------------  Example  ----------------------------
    gap> ReadPackage("HAPprime", "tst/testall.g");
    + HAPprime version 0.3.2 general tests
    + GAP4stones: 371057
    + HAPprime version 0.3.2 userguide examples
    + GAP4stones: 387662
    + HAPprime version 0.3.2 datatypes reference manual examples
    + GAP4stones: 382653
    true
  ------------------------------------------------------------------
  
  The  number  of  GAP4stones  will  vary  depending  on your machine, but any
  additional lines of messages indicate problems with your installation.
  
  The test routine calls a set of test files 'Reference: Test Files' which can
  be  found  in  the  tst  directory  of the HAPprime installation. All of the
  routines  listed  in this user guide are tested, as are many of those in the
  datatype reference manual.
  
  
  1.5 Documentation
  
  The  documentation  for  HAPprime is in two parts. This document is the user
  guide,  which covers the main functions provided by HAPprime and examples of
  their  use.  There  is  also  a  more technical HAPprime datatypes reference
  manual  which  gives  details  of  the  new  GAP  datatypes defined and used
  internally  by  HAPprime,  as  well  as outlining the algorithms used by the
  package.
  
  1.5-1 MakeHAPprimeDoc
  
  > MakeHAPprimeDoc( [manual-name] ) _________________________________function
  Returns:  nothing
  
  The  two  manuals supplied with HAPprime - this user guide and the datatypes
  reference manual - are written using the GAPDoc package and are available in
  PDF,  HTML  and  text  format.  It  should not be necessary to rebuild these
  files, but should you wish to do so then this can be done using the function
  MakeHAPprimeDoc.
  
  The  optional  argument  manual-name is a string specifying which manuals to
  build. It may be one of the following
  
  --    "all" builds both manuals. This is the default
  
  --    "userguide" builds just the user guide
  
  --    "datatypes" builds just the datatypes reference manual
  
  --    "internal"  builds  both manuals, including the otherwise undocumented
        internal functions
  
  --    "testexamples"  builds  neither  manual, but tests all of the examples
        using TestManualExamples (GAPDoc: TestManualExamples)
  
  As  well  as building the manuals, this function at the same time builds GAP
  test  files  'Reference:  Test  Files'  which means that all of the testable
  examples in the manuals are added to the HAPprime test routines described in
  Section 1.4.
  
  
  1.6 Displaying progress and calculation information
  
  By  default,  the  functions  in  HAPprime  display  no  output  (except for
  returning the result). The InfoHAPprime info class can be used to enable the
  printing  of  progress  and calculation information during processing. Since
  some  computations  with  HAPprime can take several hours, setting this to a
  higher  level  can  be  particularly  useful  for monitoring the progress of
  computations.
  
  1.6-1 InfoHAPprime
  
  > InfoHAPprime____________________________________________________info class
  
  The  InfoHAPprime  info  class  is used throughout the HAPprime package. Use
  SetInfoLevel(InfoHAPprime,  level)  to  change  the  amount  of  information
  displayed   about   the   progress  of  the  computation  (see  SetInfoLevel
  (Reference:  SetInfoLevel)  in  the  GAP  reference  manual).  The different
  distinct levels are:
  
  --    0 print nothing (this is the default)
  
  --    1   print   some   information,  mainly  progress  information  during
        computations that may take some time
  
  --    2  print  more  detailed  information,  incluing  details  of internal
        calculations