Quelle appendix.xml Sprache: XML

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



<Appendix Label="FileOverview">
<Heading>Overview of the &homalg; Package Source Code</Heading>

The &homalg; package reached more than 50.000 lines of &GAP4; code
(excluding the documentation) before the first release was made. To
keep this amount of code tracebale, the package was split in several
files.

<Section Label="The Basic Objects">

<Heading>The Basic Objects</Heading>

<Table Align="l|l">
<Caption><E>The &homalg; package files (continued)</E></Caption>

<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

<HorLine/>

<Row>
  <Item><F>HomalgObject</F></Item>
  <Item>objects of Abelian categories</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgSubobject</F></Item>
  <Item>subobject of objects of Abelian categories</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgMorphism</F></Item>
  <Item>morphisms of Abelian categories</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgElement</F></Item>
  <Item>elements are morphisms from <Q>structure objects</Q></Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgFiltration</F></Item>
  <Item>filtrations of objects of Abelian categories</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgComplex</F></Item>
  <Item>(co)complexes of objects or of (co)complexes</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgChainMorphism</F></Item>
  <Item>chain morphisms of (co)complexes</Item>
</Row>

<Row>
  <Item></Item>
  <Item>consisting of morphisms or chain morphisms</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgBicomplex</F></Item>
  <Item>bicomplexes of objects or of (co)complexes</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgBigradedObject</F></Item>
  <Item>(differential) bigraded objects</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgSpectralSequence</F></Item>
  <Item>homological and cohomological</Item>
</Row>

<Row>
  <Item></Item>
  <Item>spectral sequences</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgFunctor</F></Item>
  <Item>constructors of (multi) functors of</Item>
</Row>

<Row>
  <Item></Item>
  <Item>Abelian categories,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>left derivation of covariant functors,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>right derivation of contravariant functors,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>left satellites of covariant functors,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>right satellites of contravariant functors,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>and composition of functors</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>HomalgDiagram</F></Item>
  <Item>basic diagrams</Item>
</Row>

</Table>

</Section>

<Section Label="High Level Homological Algorithms">

<Heading>The High Level Homological Algorithms</Heading>

<Table Align="l|l">
<Caption><E>The &homalg; package files (continued)</E></Caption>
<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

<HorLine/>

<Row>
  <Item><F>StaticObjects</F></Item>
  <Item>subfactors, syzygy objects, shorten resolutions,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>saturations</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>Morphisms</F></Item>
  <Item>resolutions, (co)kernel sequences</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>Complexes</F></Item>
  <Item>(co)homology, horse shoe lemma, connecting</Item>
</Row>

<Row>
  <Item></Item>
  <Item>homomorphisms, Cartan-Eilenberg resolution</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>ChainMorphisms</F></Item>
  <Item>(co)homology</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>SpectralSequences</F></Item>
  <Item>Grothendieck bicomplexes associated to two</Item>
</Row>

<Row>
  <Item></Item>
  <Item>composable functors, spectral sequences</Item>
</Row>

<Row>
  <Item></Item>
  <Item>of bicomplexes, Grothendieck spectral sequences</Item>
</Row>

<Row>
  <Item><F>Filtrations</F></Item>
  <Item>spectral filtrations, i.e. filtrations induced</Item>
</Row>

<Row>
  <Item></Item>
  <Item>by spectral sequences of bicomplexes,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>purity filtration</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>ToolFunctors</F></Item>
  <Item>composition, addition, substraction,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>stacking, augmentation, and post dividing maps</Item>
</Row>

<Row>
  <Item><F>BasicFunctors</F></Item>
  <Item>kernel, defect of exactness</Item>
</Row>

<Row>
  <Item><F>OtherFunctors</F></Item>
  <Item>torsion submodule, torsion free factor,</Item>
</Row>

<Row>
  <Item></Item>
  <Item>pullback, pushout, Auslander dual</Item>
</Row>

</Table>

</Section>

<Section Label="Logical Implications">

<Heading>Logical Implications for &homalg; Objects</Heading>

<Table Align="l|l">
<Caption><E>The &homalg; package files (continued)</E></Caption>
<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

<HorLine/>

<Row>
  <Item><F>LIOBJ</F></Item>
  <Item>logical implications for objects of an Abelian category</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>LIMOR</F></Item>
  <Item>logical implications for morphisms of an Abelian category</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

<Row>
  <Item><F>LICPX</F></Item>
  <Item>logical implications for complexes</Item>
</Row>

<Row><Item></Item><Item></Item></Row>

</Table>

</Section>

</Appendix>

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