<!-- 
  HAPPRIME - internal.xml.in
  Function documentation template file for HAPprime
  Paul Smith

  Copyright (C)  2008
  National University of Ireland Galway
  Copyright (C)  2011
  University of St Andrews
-->

<!-- ********************************************************** -->
<Chapter  Label="InternalFunctions">
  <Heading>Internal functions</Heading>

  <Section Label="InternalGGenerators">
    <Heading>Matrices as &G;-generators of a &FG;-module vector space</Heading>

    Both <K>FpGModuleGF</K> (Chapter <Ref Chap="FpGModuleGF"/>) and 
    <K>FpGModuleHomomorphismGF</K> 
    (Chapter <Ref Chap="FpGModuleGFHom"/>) 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.

    <!-- GAPDocSourceSuffix="_manGenMatInt" -->

  </Section>
  
  <Section>
    <Heading>&FG;-modules</Heading>

    &FG;-modules in &HAPprime; use the datatype <K>FpGModuleGF</K> 
    (Chapter <Ref Chap="FpGModuleGF"/>). Internally, this uses many of the 
    functions listed in Section <Ref Sect="InternalGGenerators"/>, and
    further internal functions are listed below.

    <!-- GAPDocSourceSuffix="_DTmanFpGModuleInt" -->

  </Section>
  
  <Section>
    <Heading>Resolutions</Heading>

    For details of the main resolution functions in &HAPprime;, see Chapter
    <Ref Chap="Resolution"/> of this datatypes reference manual, and 
    <Ref Sect="Resolutions" BookName="HAPprime"/> in the &HAPprime; user guide.
    This section describes the internal helper functions used by the 
    higher-level functions.

    <!-- GAPDocSourceSuffix="_DTmanResolutionInt" -->

  </Section>
  
  <Section>
    <Heading>Test functions</Heading>

    Internal helper functions for testing &HAPprime;.

    <!-- GAPDocSourceSuffix="_manTestInt" -->

  </Section>
  
</Chapter>

