3 Functions for Homological Algebra
3.1 Resolutions
3.1-1 ResolutionPrimePowerGroup
| > ResolutionPrimePowerGroupRadical( G, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupGF( G, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupAutoMem( G, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupGF2( G, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupRadical( M, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupGF( M, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupAutoMem( M, n ) | ( operation ) | 
| > ResolutionPrimePowerGroupGF2( M, n ) | ( operation ) | 
Returns: HAPResolution
Returns n terms of a minimal free FG-resolution for either the ground ring of a prime power group G or of a module M. For the module version, M must be passed as an FpGModuleGF object - see HAPprime Datatypes: FG-modules in the HAPprime datatypes reference manual.
Three versions of this function are provided:
- ResolutionPrimePowerGroupRadical
- uses the same resolution-building method as the HAP function - ResolutionPrimePowerGroup, but stores the resolution in a different format that takes only about half the memory of the HAP version.
 
- ResolutionPrimePowerGroupGF
- calculates the resolution using HAPprime's G-generator form of modules, which reduces memory use by around a factor of two over - ResolutionPrimePowerGroupRadical, but is slower by an order of magnitude.
 
- ResolutionPrimePowerGroupAutoMem
- automatically switches between the two previous versions based on the available memory. It uses the - Radicalversion until it gets close to the limit of the available memory, and then switches to the- GFversion.
 
- ResolutionPrimePowerGroupGF2
- calculates the resolution by FG-matrix partitioning. The amount of partitioning is governed by the Reference: Options Stack option - MaxFGExpansionSize. The default value means that until the boundary map takes about 128Mb, the method is equivalent to- ResolutionPrimePowerGroupRadical, and then it tends towards- ResolutionPrimePowerGroupGFin terms of time, but saves less memory.
 
See the HAPprime datatypes reference manual for details of the different algorithms, in particular the chapters on the G-generator form of FG-modules HAPprime Datatypes: FG-modules and FG-module homomorphisms HAPprime Datatypes: FG-module homomorphisms and on resolutions HAPprime Datatypes: Resolutions.
3.1-2 ExtendResolutionPrimePowerGroup
| > ExtendResolutionPrimePowerGroupRadical( R ) | ( operation ) | 
| > ExtendResolutionPrimePowerGroupGF( R ) | ( operation ) | 
| > ExtendResolutionPrimePowerGroupAutoMem( R ) | ( operation ) | 
| > ExtendResolutionPrimePowerGroupGF2( R ) | ( operation ) | 
Returns: HAPResolution
Returns the resolution R extended by one term. The three variants offer a choice between memory and speed, and correspond to the different versions of ResolutionPrimePowerGroup in HAPprime. See the documentation (above) for those functions for a description of the different variants.