Internal functions
Matrices as &G;-generators of a &FG;-module vector space

Both FpGModuleGF (Chapter ) and FpGModuleHomomorphismGF (Chapter ) store a matrix whose rows are &G;-generators for a module vector space (the module and the homomorphism's image respectively). The internal functions listed here provide common operations for dealing with these matrices.

<#Include Label="HAPPRIME_ValueOptionMaxFGExpansionSize_manGenMatInt"> <#Include Label="HAPPRIME_KernelOfGeneratingRowsDestructive_manGenMatInt"> <#Include Label="HAPPRIME_GActMatrixColumns_manGenMatInt"> <#Include Label="HAPPRIME_ExpandGeneratingRows_manGenMatInt"> <#Include Label="HAPPRIME_AddGeneratingRowToSemiEchelonBasisDestructive_manGenMatInt"> <#Include Label="HAPPRIME_ReduceVectorDestructive_manGenMatInt"> <#Include Label="HAPPRIME_ReduceGeneratorsOfModuleBySemiEchelonDestructive_manGenMatInt"> <#Include Label="HAPPRIME_DisplayGeneratingRows_manGenMatInt"> <#Include Label="HAPPRIME_GeneratingRowsBlockStructure_manGenMatInt"> <#Include Label="HAPPRIME_DisplayGeneratingRowsBlocks_manGenMatInt"> <#Include Label="HAPPRIME_IndependentGeneratingRows_manGenMatInt"> <#Include Label="HAPPRIME_GactFGvector_manGenMatInt"> <#Include Label="HAPPRIME_CoefficientsOfGeneratingRowsDestructive_manGenMatInt"> <#Include Label="HAPPRIME_GenerateFromGeneratingRowsCoefficients_manGenMatInt"> <#Include Label="HAPPRIME_RemoveZeroBlocks_manGenMatInt"> <#Include Label="HAPPRIME_AddZeroBlocks_manGenMatInt">

&FG;-modules

&FG;-modules in &HAPprime; use the datatype FpGModuleGF (Chapter ). Internally, this uses many of the functions listed in Section , and further internal functions are listed below.

<#Include Label="HAPPRIME_DirectSumForm_DTmanFpGModuleInt"> <#Include Label="HAPPRIME_PrintModuleDescription_DTmanFpGModuleInt"> <#Include Label="HAPPRIME_ModuleGeneratorCoefficients_DTmanFpGModuleInt"> <#Include Label="HAPPRIME_ModuleElementFromGeneratorCoefficients_DTmanFpGModuleInt"> <#Include Label="HAPPRIME_MinimalGeneratorsVectorSpaceGeneratingRowsDestructive_DTmanFpGModuleInt"> <#Include Label="HAPPRIME_IsGroupAndAction_DTmanFpGModuleInt">

Resolutions

For details of the main resolution functions in &HAPprime;, see Chapter of this datatypes reference manual, and in the &HAPprime; user guide. This section describes the internal helper functions used by the higher-level functions.

<#Include Label="HAPPRIME_WordToVector_DTmanResolutionInt"> <#Include Label="HAPPRIME_VectorToWord_DTmanResolutionInt"> <#Include Label="HAPPRIME_BoundaryMatrices_DTmanResolutionInt"> <#Include Label="HAPPRIME_AddNextResolutionBoundaryMapMatNC_DTmanResolutionInt"> <#Include Label="HAPPRIME_CreateResolutionWithBoundaryMapMatsNC_DTmanResolutionInt">

Test functions

Internal helper functions for testing &HAPprime;.

<#Include Label="HAPPRIME_SingularIsAvailable_manTestInt"> <#Include Label="HAPPRIME_Random2Group_manTestInt"> <#Include Label="HAPPRIME_TestResolutionPrimePowerGroup_manTestInt">