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

  Copyright (C)  2007
  National University of Ireland Galway
  Copyright (C)  2011
  University of St Andrews
-->

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<Chapter>
  <Heading>Function Reference</Heading>

  <Section>
    <Heading>Matrices as generators of a row space</Heading>

    <Package>HAPprime</Package> represents <M>\mathbb{F}G</M>-modules as
    vector spaces and makes use of standard &GAP; operations and datatypes to 
    store and manipulate them. There are a few particular variants of functions 
    that are not provided as part &GAP;, and they are described here.

    <!-- GAPDocSourceSuffix="_manBaseMat" -->

  </Section>

  <Section Label="FG modules">
    <Heading><M>\mathbb{F}G</M>-modules</Heading>

    <!-- GAPDocSourceSuffix="_manFpGModule" -->

  </Section>

  <Section Label="FG module homomorphisms">
    <Heading><M>\mathbb{F}G</M>-module homomorphisms</Heading>


    <!-- GAPDocSourceSuffix="_manFpGModuleHom" -->

  </Section>

  <Section>
    <Heading>Resolutions</Heading>

    <!-- GAPDocSourceSuffix="_manResolution" -->

  </Section>

  <Section>
    <Heading>Ring structure</Heading>

    <!-- GAPDocSourceSuffix="_manRings" -->

  </Section>

  <Section>
    <Heading>Polynomials</Heading>

    <!-- GAPDocSourceSuffix="_manPolynomial" -->

  </Section>

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

    <!-- GAPDocSourceSuffix="_manTest" -->

  </Section>

  <Section>
    <Heading>Miscellaneous functions</Heading>

    <!-- GAPDocSourceSuffix="_manMisc" -->

  </Section>

</Chapter>


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<Chapter>
  <Heading>Internal Function Reference</Heading>

  These are functions that are used internally in <Package>HAPprime</Package>.
  They should not be needed by users of the package, but may be useful to 
  developers and are provided for completeness

  <Section>
    <Heading>Matrices as <M>g</M>-generators of a row space</Heading>

    Both <K>FpGModuleGF</K> and <K>FpGModuleHomomorphismGF</K> store a matrix 
    whose rows are <M>g</M>-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><M>\mathbb{F}G</M>-modules</Heading>

    Internal helper functions for <K>FpGModuleGFs</K>s.

    <!-- GAPDocSourceSuffix="_manFpGModuleInt" -->

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

    Internal helper functions for building resolutions.

    <!-- GAPDocSourceSuffix="_manResolutionInt" -->

  </Section>
  
  <Section>
    <Heading>Miscellaneous</Heading>

    Miscellaneous internal helper functions.

    <!-- GAPDocSourceSuffix="_manMiscInt" -->

  </Section>
  
</Chapter>

