  
  [1X1 Introduction[0X
  
  The  [5XHAPprime[0m  package  is  a  [5XGAP[0m package which supplements the [5XHAP[0m package
  ([7Xhttp://hamilton.nuigalway.ie/Hap/www/[0m),    providing   new   and   improved
  functions  for  doing  homological  algebra over small prime-power groups. A
  detailed  overview  of the [5XHAPprime[0m package, with examples and documentation
  of  the  high-level functions, is provided in the accompanying [5XHAPprime[0m user
  guide.
  
  This document, the datatypes reference manual, supplements the [5XHAPprime[0m user
  guide.  It  describes the new [5XGAP[0m datatypes defined by the [5XHAPprime[0m package,
  and  all  of  the  associated  functions  for  working  with  each  of these
  datatypes. The datatypes are
  
  [8X[9XFpGModuleGF[0m[8X[0m
        (Chapter  [14X5[0m)  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.
  
  [8X[9XFpGModuleHomomorphismGF[0m[8X[0m
        (Chapter  [14X6[0m)  a  free linear homomorphism between two FG-modules, each
        represented  as  a  [9XFpGModuleGF[0m.  this also uses the compact generator
        form to save memory in its operations.
  
  [8X[9XHAPResolution[0m[8X[0m
        (Chapter  [14X2[0m)  this  datatype, defined in the [5XHAP[0m package, represents a
        free  FG-resolution of a FG-module. [5XHAPprime[0m extends the definition of
        this  datatype  to  save  memory, and provides additional functions to
        operate on resolutions.
  
  [8X[9XHAPDerivation[0m[8X[0m
        (Chapter  [14X8[0m)  a  derivation  over  a polynomial ring R. In particular,
        [5XHAPprime[0m  provides  functions  to calculate the kernel and homology of
        derivations for polynomials over prime fields.
  
  In  addition,  Chapter  [14X10[0m provides documentation for some general functions
  defined  in  [5XHAPprime[0m  which  extend  some of the basic [5XGAP[0m 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.
  
