1 Introduction
  
  The  HAPprime  package  is  a  GAP package which supplements the HAP package
  (http://hamilton.nuigalway.ie/Hap/www/),    providing   new   and   improved
  functions  for  doing  homological  algebra over small prime-power groups. A
  detailed  overview  of the HAPprime package, with examples and documentation
  of  the  high-level functions, is provided in the accompanying HAPprime user
  guide.
  
  This document, the datatypes reference manual, supplements the HAPprime user
  guide.  It  describes the new GAP datatypes defined by the HAPprime package,
  and  all  of  the  associated  functions  for  working  with  each  of these
  datatypes. The datatypes are
  
  FpGModuleGF
        (Chapter  5)  a  free  FG-module  compactly  represented  in  terms of
        generating  elements,  with operations that do as much manipulation as
        possible within this form, thus minimizing memory use.
  
  FpGModuleHomomorphismGF
        (Chapter  6)  a  free linear homomorphism between two FG-modules, each
        represented  as  a  FpGModuleGF.  this also uses the compact generator
        form to save memory in its operations.
  
  HAPResolution
        (Chapter  2)  this  datatype, defined in the HAP package, represents a
        free  FG-resolution of a FG-module. HAPprime extends the definition of
        this  datatype  to  save  memory, and provides additional functions to
        operate on resolutions.
  
  HAPDerivation
        (Chapter  8)  a  derivation  over  a polynomial ring R. In particular,
        HAPprime  provides  functions  to calculate the kernel and homology of
        derivations for polynomials over prime fields.
  
  In  addition,  Chapter  10 provides documentation for some general functions
  defined  in  HAPprime  which  extend  some of the basic GAP functionality in
  areas such as matrices and polynomials.
  
  Each  chapter  of  this  reference  manual  begins  with  an overview of the
  datatype,  and then implementation details of any interesting functions. The
  function  reference  of  related  functions  then  follows,  subdivided into
  sections  of  related  functions.  Examples  demonstrating  the  use of each
  function are given at the end of each section.