  
  [1X3 [33X[0;0YFunctions for Homological Algebra[133X[101X
  
  
  [1X3.1 [33X[0;0YResolutions[133X[101X
  
  
  [1X3.1-1 [33X[0;0YResolutionPrimePowerGroup[133X[101X
  
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupRadical[102X( [3XG[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupGF[102X( [3XG[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupAutoMem[102X( [3XG[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupGF2[102X( [3XG[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupRadical[102X( [3XM[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupGF[102X( [3XM[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupAutoMem[102X( [3XM[103X, [3Xn[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XResolutionPrimePowerGroupGF2[102X( [3XM[103X, [3Xn[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Y[9XHAPResolution[109X[133X
  
  [33X[0;0YReturns  [3Xn[103X  terms of a minimal free [22XFG[122X-resolution for either the ground ring
  of a prime power group [3XG[103X or of a module [3XM[103X. For the module version, [3XM[103X must be
  passed  as  an  [9XFpGModuleGF[109X object - see [14X'HAPprime Datatypes: FG-modules'[114X in
  the [5XHAPprime[105X datatypes reference manual.[133X
  
  [33X[0;0YThree versions of this function are provided:[133X
  
  [8X[9XResolutionPrimePowerGroupRadical[109X[108X
        [33X[0;6Yuses   the   same  resolution-building  method  as  the  [5XHAP[105X  function
        [2XResolutionPrimePowerGroup[102X ([14XHAP: ResolutionPrimePowerGroup[114X), but stores
        the  resolution  in  a different format that takes only about half the
        memory of the [5XHAP[105X version.[133X
  
  [8X[9XResolutionPrimePowerGroupGF[109X[108X
        [33X[0;6Ycalculates   the  resolution  using  [5XHAPprime[105X's  [22XG[122X-generator  form  of
        modules,  which  reduces  memory  use  by  around a factor of two over
        [9XResolutionPrimePowerGroupRadical[109X,   but  is  slower  by  an  order  of
        magnitude.[133X
  
  [8X[9XResolutionPrimePowerGroupAutoMem[109X[108X
        [33X[0;6Yautomatically  switches between the two previous versions based on the
        available  memory.  It uses the [10XRadical[110X version until it gets close to
        the  limit  of  the  available  memory,  and  then  switches to the [10XGF[110X
        version.[133X
  
  [8X[9XResolutionPrimePowerGroupGF2[109X[108X
        [33X[0;6Ycalculates  the  resolution  by  [22XFG[122X-matrix partitioning. The amount of
        partitioning  is  governed  by  the  [14X'Reference: Options Stack'[114X option
        [10XMaxFGExpansionSize[110X.  The  default  value means that until the boundary
        map    takes    about    128Mb,    the   method   is   equivalent   to
        [9XResolutionPrimePowerGroupRadical[109X,    and   then   it   tends   towards
        [9XResolutionPrimePowerGroupGF[109X in terms of time, but saves less memory.[133X
  
  [33X[0;0YSee  the  [5XHAPprime[105X  datatypes  reference manual for details of the different
  algorithms, in particular the chapters on the [22XG[122X-generator form of [22XFG[122X-modules
  [14X'HAPprime  Datatypes:  FG-modules'[114X  and  [22XFG[122X-module  homomorphisms  [14X'HAPprime
  Datatypes:  FG-module homomorphisms'[114X and on resolutions [14X'HAPprime Datatypes:
  Resolutions'[114X.[133X
  
  
  [1X3.1-2 [33X[0;0YExtendResolutionPrimePowerGroup[133X[101X
  
  [33X[1;0Y[29X[2XExtendResolutionPrimePowerGroupRadical[102X( [3XR[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XExtendResolutionPrimePowerGroupGF[102X( [3XR[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XExtendResolutionPrimePowerGroupAutoMem[102X( [3XR[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XExtendResolutionPrimePowerGroupGF2[102X( [3XR[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Y[9XHAPResolution[109X[133X
  
  [33X[0;0YReturns  the  resolution  [3XR[103X extended by one term. The three variants offer a
  choice between memory and speed, and correspond to the different versions of
  [9XResolutionPrimePowerGroup[109X  in  [5XHAPprime[105X.  See  the documentation ([14X3.1-1[114X) for
  those functions for a description of the different variants.[133X
  
