<?xml version="1.0" encoding="utf-8"?>

<!DOCTYPE Book SYSTEM "gapdoc.dtd">


<Book Name="HAP commands">

<TitlePage>
  <Title>Homological Algebra Programming</Title>
  <Subtitle>HAP</Subtitle>
  <Version>Version <#Include SYSTEM "../version"></Version>
  <Author>Graham Ellis 
          <Email>Graham.Ellis@nuigalway.ie</Email> 
  </Author>
  <Date><#Include SYSTEM "../date"></Date>
  <Address>
  School of Mathematics<Br/> National University of Irelnd, Galway 
  <Br/> Galway<Br/> (Ireland)
  </Address>
  <Abstract>
<B>HAP</B> is a homological algebra library for use with the GAP computer algebra 
system, and is still under development. The current version 
<#Include SYSTEM "../version"> was released on <#Include SYSTEM "../date">.

<Br/>

The initial focus of the library was on computations related to the cohomology of finite and infinite groups, with particular emphasis on integral coefficients. The focus has since broadened to include Steenrod algebras of finite groups, Bredon homology, cohomology of simplicial groups, and general computations in algebraic topology relating to finite CW-complexes, covering spaces, knots, knotted surfaces, and topics such as persitent homology arising in topological data analysis.

<Br/>This document describes the functions available in <B>HAP</B>. Examples illustrating these functions are available in the <URL><Link>../tutorial/chap0.html</Link><LinkText><B>HAP</B> tutorial</LinkText></URL>.
  </Abstract>
  <Copyright>&copyright; 2005-2019 by Graham Ellis 
  </Copyright>
  <Acknowledgements>The HAP project has been supported by the School of Maths at NUI Galway, various PhD students and postdoctoral researchers at NUI Galway, the Irish Research Council, Science Foundation Ireland, and the EU Marie Curie programme.
  </Acknowledgements>
</TitlePage>

<TableOfContents/>

<Body>
 <#Include SYSTEM "newNewCellComplexes.xml">
 <#Include SYSTEM "newNewResolutions.xml">
 <#Include SYSTEM "newNewGroups.xml">
<#Include SYSTEM "newNewParallel.xml">

 <#Include SYSTEM "newResolutions.xml">
 <#Include SYSTEM "newModuleResolutions.xml">
 <#Include SYSTEM "newInducedChainMaps.xml">
 <#Include SYSTEM "newFunctors.xml">
 <#Include SYSTEM "newChainComplexes.xml">
 <#Include SYSTEM "newSparse.xml">
 <#Include SYSTEM "newHomology.xml">
 <#Include SYSTEM "newPoincare.xml">
 <#Include SYSTEM "newRings.xml">
 <#Include SYSTEM "newHAPprime.xml">
 <#Include SYSTEM "newNonabelian.xml">
 <#Include SYSTEM "newLie.xml">
 <#Include SYSTEM "newPresentations.xml">
 <#Include SYSTEM "newOrbits.xml">
 <#Include SYSTEM "newCocycles.xml">
 <#Include SYSTEM "newWords.xml">
 <#Include SYSTEM "newFpgmodules.xml">
 <#Include SYSTEM "newMeataxe.xml">
 <#Include SYSTEM "newGouter.xml">
 <#Include SYSTEM "newCat1groups.xml">
 <#Include SYSTEM "newSimplicialGroups.xml">
 <#Include SYSTEM "newCoxeter.xml">
 <#Include SYSTEM "newTorsionSubcomplexes.xml">
 <#Include SYSTEM "newSimplicial.xml">
 <#Include SYSTEM "newCubical.xml">
 <#Include SYSTEM "newCW.xml">
 <#Include SYSTEM "newKnots.xml">
 <#Include SYSTEM "newFunctionsKnotsQuandles.xml">
 <#Include SYSTEM "newMetrics.xml">
 <#Include SYSTEM "newCategories.xml">
 <#Include SYSTEM "newPseudolists.xml">
 <#Include SYSTEM "newParallel.xml">
 <#Include SYSTEM "newAccess.xml">
 <#Include SYSTEM "newMiscellaneous.xml">
 <#Include SYSTEM "Undocumented.xml">


</Body>

<TheIndex/>

</Book>

