  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThe  [5XHAPprime[105X  package  is  a  [5XGAP[105X package which supplements the [5XHAP[105X package
  ([7Xhttp://hamilton.nuigalway.ie/Hap/www/[107X),    providing   new   and   improved
  functions  for  doing  homological  algebra over small prime-power groups. A
  detailed  overview  of the [5XHAPprime[105X package, with examples and documentation
  of  the  high-level functions, is provided in the accompanying [5XHAPprime[105X user
  guide.[133X
  
  [33X[0;0YThis document, the datatypes reference manual, supplements the [5XHAPprime[105X user
  guide.  It  describes the new [5XGAP[105X datatypes defined by the [5XHAPprime[105X package,
  and  all  of  the  associated  functions  for  working  with  each  of these
  datatypes. The datatypes are[133X
  
  [8X[9XHAPResolution[109X[108X
        [33X[0;6Y(Chapter  [14X2[114X)  this  datatype, defined in the [5XHAP[105X package, represents a
        free  [22XFG[122X-resolution of a [22XFG[122X-module. [5XHAPprime[105X extends the definition of
        this  datatype  to  save  memory, and provides additional functions to
        operate on resolutions.[133X
  
  [8X[9XFpGModuleGF[109X[108X
        [33X[0;6Y(Chapter  [14X3[114X)  a  free  [22XFG[122X-module  compactly  represented  in  terms of
        generating  elements,  with operations that do as much manipulation as
        possible within this form, thus minimizing memory use.[133X
  
  [8X[9XFpGModuleHomomorphismGF[109X[108X
        [33X[0;6Y(Chapter  [14X4[114X)  a  free linear homomorphism between two [22XFG[122X-modules, each
        represented  as  a  [9XFpGModuleGF[109X.  this also uses the compact generator
        form to save memory in its operations.[133X
  
  [33X[0;0YIn  addition,  Chapter  [14X5[114X  provides documentation for some general functions
  defined  in  [5XHAPprime[105X  which  extend  some of the basic [5XGAP[105X functionality in
  areas such as matrices and polynomials.[133X
  
  [33X[0;0YEach  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.[133X
  
  [33X[0;0YEarlier  versions  of  this  datatypes  reference manual also documented the
  datatypes  [9XGradedAlgebraPresentation[109X, [9XHAPRingHomomorphism[109X and [9XHAPDerivation[109X.
  The  definitions of these datatypes and their related functions are now part
  of [5XHAP[105X and will be documented as part of that package.[133X
  
  
  [1X1.1 [33X[0;0YInternal function reference[133X[101X
  
  [33X[0;0YThis  version  of the datatypes reference manual has been specially built to
  also  provide  documentation  for all of the internal functions of [5XHAPprime[105X.
  (This  can be done using the optional argument to [2XMakeHAPprimeDoc[102X ([14XHAPprime:
  MakeHAPprimeDoc[114X).) The documentation for these functions is found in Chapter
  [14X6[114X.[133X
  
