<Chapter><Heading>Cellular complexes</Heading>

Data <M>\longrightarrow</M> Cellular Complexes

<Table Align="|l|" >


<Row> <Item>
<Index>HenonOrbit</Index>
<#Include SYSTEM "newman/RegularCWPolytope.xml"> </Item> </Row>

<Row> <Item>
<Index>CubicalComplex</Index>
<#Include SYSTEM "newman/CubicalComplex.xml"> </Item> </Row>


<Row> <Item>
<Index>PureCubicalComplex</Index>
<#Include SYSTEM "newman/PureCubicalComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>PureCubicalKnot</Index>
<#Include SYSTEM "newman/PureCubicalKnot.xml"> </Item> </Row>

<Row> <Item>
<Index>PurePermutahedralKnot</Index>
<#Include SYSTEM "newman/PurePermutahedralKnot.xml"> </Item> </Row>

<Row> <Item>
<Index>PurePermutahedralComplex</Index>
<#Include SYSTEM "newman/PurePermutahedralComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>CayleyGraphOfGroup</Index>
<#Include SYSTEM "newman/CayleyGraphOfGroup.xml"> </Item> </Row>

<Row> <Item>
<Index>EquivariantEuclideanSpace</Index>
<#Include SYSTEM "newman/EquivariantEuclideanSpace.xml"> </Item> </Row>

<Row> <Item>
<Index>EquivariantOrbitPolytope</Index>
<#Include SYSTEM "newman/EquivariantOrbitPolytope.xml"> </Item> </Row>

<Row> <Item>
<Index>EquivariantTwoComplex</Index>
<#Include SYSTEM "newman/EquivariantTwoComplex.xml"> </Item> </Row>


<Row> <Item>
<Index>QuillenComplex</Index>
<#Include SYSTEM "newman/QuillenComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>RestrictedEquivariantCWComplex</Index>
<#Include SYSTEM "newman/RestrictedEquivariantCWComplex.xml"> </Item> </Row>


<Row> <Item>
<Index>RandomSimplicialGraph</Index>
<#Include SYSTEM "newman/RandomSimplicialGraph.xml"> </Item> </Row>

<Row> <Item>
<Index>RandomSimplicialTwoComplex</Index>
<#Include SYSTEM "newman/RandomSimplicialTwoComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadCSVfileAsPureCubicalKnot</Index>
<#Include SYSTEM "newman/ReadCSVfileAsPureCubicalKnot.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadImageAsPureCubicalComplex</Index>
<#Include SYSTEM "newman/ReadImageAsPureCubicalComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadImageAsFilteredPureCubicalComplex</Index>
<#Include SYSTEM "newman/ReadImageAsFilteredPureCubicalComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadImageAsWeightFunction</Index>
<#Include SYSTEM "newman/ReadImageAsWeightFunction.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadPDBfileAsPureCubicalComplex</Index>
<#Include SYSTEM "newman/ReadPDBfileAsPureCubicalComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ReadPDBfileAsPurePermutahedralComplex</Index>
<#Include SYSTEM "newman/ReadPDBfileAsPurePermutahedralComplex.xml"> </Item> </Row>



<Row> <Item> 
<Index>RegularCWPolytope</Index> 
<#Include SYSTEM "newman/RegularCWPolytope.xml"> </Item> </Row>

<Row> <Item> 
<Index>SimplicialComplex</Index>
<#Include SYSTEM "newman/SimplicialComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>SymmetricMatrixToFilteredGraph</Index>
<#Include SYSTEM "newman/SymmetricMatrixToFilteredGraph.xml"> </Item> </Row>

<Row> <Item>
<Index>SymmetricMatrixToGraph</Index>
<#Include SYSTEM "newman/SymmetricMatrixToGraph.xml"> </Item> </Row>


</Table>

Metric Spaces

<Table Align="|l|" >

<Row> <Item>
<Index>CayleyMetric</Index>
<#Include SYSTEM "newman/CayleyMetric.xml"> </Item> </Row>

<Row> <Item>
<Index>EuclideanMetric</Index>
<#Include SYSTEM "newman/EuclideanMetric.xml"> </Item> </Row>


<Row> <Item>
<Index>EuclideanSquaredMetric</Index>
<#Include SYSTEM "newman/EuclideanSquaredMetric.xml"> </Item> </Row>


<Row> <Item>
<Index>HammingMetric</Index>
<#Include SYSTEM "newman/HammingMetric.xml"> </Item> </Row>

<Row> <Item>
<Index>KendallMetric</Index>
<#Include SYSTEM "newman/KendallMetric.xml"> </Item> </Row>

<Row> <Item>
<Index>ManhattanMetric</Index>
<#Include SYSTEM "newman/ManhattanMetric.xml"> </Item> </Row>




<Row> <Item>
<Index>VectorsToSymmetricMatrix</Index>
<#Include SYSTEM "newman/VectorsToSymmetricMatrix.xml"> </Item> </Row>

</Table>


Cellular Complexes <M>\longrightarrow</M> Cellular Complexes

<Table Align="|l|" >

<Row> <Item>
<Index>BoundaryMap</Index>
<#Include SYSTEM "newman/BoundaryMap.xml"> </Item> </Row>


<Row> <Item>
<Index>CliqueComplex</Index>
<#Include SYSTEM "newman/CliqueComplex.xml"> </Item> </Row>


<Row> <Item>
<Index>ConcentricFiltration</Index>
<#Include SYSTEM "newman/ConcentricFiltration.xml"> </Item> </Row>

<Row> <Item>
<Index>DirectProduct</Index>
<#Include SYSTEM "newman/DirectProduct.xml"> </Item> </Row>

<Row> <Item>
<Index>FiltrationTerm</Index>
<#Include SYSTEM "newman/FiltrationTerm.xml"> </Item> </Row>


<Row> <Item>
<Index>Graph</Index>
<#Include SYSTEM "newman/Graph.xml"> </Item> </Row>

<Row> <Item>
<Index>HomotopyGraph</Index>
<#Include SYSTEM "newman/HomotopyGraph.xml"> </Item> </Row>


<Row> <Item> 
<Index>Nerve</Index>
<#Include SYSTEM "newman/Nerve.xml"> </Item> </Row>

<Row> <Item> 
<Index>RegularCWComplex</Index>
<#Include SYSTEM "newman/RegularCWComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>RegularCWMap</Index>
<#Include SYSTEM "newman/RegularCWMap.xml"> </Item> </Row>

<Row> <Item>
<Index>ThickeningFiltration</Index>
<#Include SYSTEM "newman/ThickeningFiltration.xml"> </Item> </Row>

</Table>

Cellular Complexes <M>\longrightarrow</M> Cellular Complexes (Preserving Data Types)
<Table Align="|l|" >
 
<Row> <Item>
<Index>ContractedComplex</Index>
<#Include SYSTEM "newman/ContractedComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ContractibleSubcomplex</Index>
<#Include SYSTEM "newman/ContractibleSubcomplex.xml"> </Item> </Row>


<Row> <Item>
<Index>KnotReflection</Index>
<#Include SYSTEM "newman/KnotReflection.xml"> </Item> </Row>

<Row> <Item>
<Index>KnotSum</Index>
<#Include SYSTEM "newman/KnotSum.xml"> </Item> </Row>

<Row> <Item>
<Index>OrientRegularCWComplex</Index>
<#Include SYSTEM "newman/OrientRegularCWComplex.xml"> </Item> </Row>


<Row> <Item>
<Index>PathComponent</Index>
<#Include SYSTEM "newman/PathComponent.xml"> </Item> </Row>

<Row> <Item>
<Index>PureComplexBoundary</Index>
<#Include SYSTEM "newman/PureComplexBoundary.xml"> </Item> </Row>


<Row> <Item>
<Index>PureComplexComplement</Index>
<#Include SYSTEM "newman/PureComplexComplement.xml"> </Item> </Row>

<Row> <Item>
<Index>PureComplexDifference</Index>
<#Include SYSTEM "newman/PureComplexDifference.xml"> </Item> </Row>


<Row> <Item>
<Index>PureComplexIntersection</Index>
<#Include SYSTEM "newman/PureComplexIntersection.xml"> </Item> </Row>

<Row> <Item>
<Index>PureComplexThickened</Index>
<#Include SYSTEM "newman/PureComplexThickened.xml"> </Item> </Row>


<Row> <Item>
<Index>PureComplexUnion</Index>
<#Include SYSTEM "newman/PureComplexUnion.xml"> </Item> </Row>

<Row> <Item>
<Index>SimplifiedComplex</Index>
<#Include SYSTEM "newman/SimplifiedComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ZigZagContractedComplex</Index>
<#Include SYSTEM "newman/ZigZagContractedComplex.xml"> </Item> </Row>



</Table>


Cellular Complexes <M>\longrightarrow</M> Homotopy Invariants 

<Table Align="|l|" >



<Row> <Item>
<Index>AlexanderPolynomial</Index>
<#Include SYSTEM "newman/AlexanderPolynomial.xml"> </Item> </Row>



<Row> <Item>
<Index>BettiNumber</Index>
<#Include SYSTEM "newman/BettiNumber.xml"> </Item> </Row>

<Row> <Item>
<Index>EulerCharacteristic</Index>
<#Include SYSTEM "newman/EulerCharacteristic.xml"> </Item> </Row>

<Row> <Item>
<Index>EulerIntegral</Index>
<#Include SYSTEM "newman/EulerIntegral.xml"> </Item> </Row>


<Row> <Item>
<Index>FundamentalGroup</Index>
<#Include SYSTEM "newman/FundamentalGroup.xml"> </Item> </Row>

<Row> <Item>
<Index>FundamentalGroupOfQuotient</Index>
<#Include SYSTEM "newman/FundamentalGroupOfQuotient.xml"> </Item> </Row>

<Row> <Item>
<Index>IsAspherical</Index>
<#Include SYSTEM "newman/IsAspherical.xml"> </Item> </Row>


<Row> <Item>
<Index>KnotGroup</Index>
<#Include SYSTEM "newman/KnotGroup.xml"> </Item> </Row>


<Row> <Item>
<Index>PiZero</Index>
<#Include SYSTEM "newman/PiZero.xml"> </Item> </Row>


<Row> <Item>
<Index>PersistentBettiNumbers</Index>
<#Include SYSTEM "newman/PersistentBettiNumbers.xml"> </Item> </Row>


</Table>

Data <M>\longrightarrow</M> Homotopy Invariants

<Table Align="|l|" >

<Row> <Item>
<Index>DendrogramMat</Index>
<#Include SYSTEM "newman/DendrogramMat.xml"> </Item> </Row>

</Table>

Cellular Complexes <M>\longrightarrow</M> Non Homotopy Invariants

<Table Align="|l|" >

<Row> <Item>
<Index>ChainComplex</Index>
<#Include SYSTEM "newman/ChainComplex.xml"> </Item> </Row>

<Row> <Item>
<Index>ChainComplexEquivalence</Index>
<#Include SYSTEM "newman/ChainComplexEquivalence.xml"> </Item> </Row>


<Row> <Item>
<Index>ChainComplexOfQuotient</Index>
<#Include SYSTEM "newman/ChainComplexOfQuotient.xml"> </Item> </Row>

<Row> <Item>
<Index>ChainMap</Index>
<#Include SYSTEM "newman/ChainMap.xml"> </Item> </Row>

<Row> <Item>
<Index>CochainComplex</Index>
<#Include SYSTEM "newman/CochainComplex.xml"> </Item> </Row>




<Row> <Item>
<Index>CriticalCells</Index>
<#Include SYSTEM "newman/CriticalCells.xml"> </Item> </Row>

<Row> <Item>
<Index>DiagonalApproximation</Index>
<#Include SYSTEM "newman/DiagonalApproximation.xml"> </Item> </Row>


<Row> <Item>
<Index>Size</Index>
<#Include SYSTEM "newman/Size.xml"> </Item> </Row>


</Table>

(Co)chain Complexes <M>\longrightarrow </M> (Co)chain Complexes

<Table Align="|l|" >

<Row> <Item>
<Index>FilteredTensorWithInteres</Index>
<#Include SYSTEM "newman/FilteredTensorWithIntegers.xml"> </Item> </Row>

<Row> <Item>
<Index>FilteredTensorWithInteresModP</Index>
<#Include SYSTEM "newman/FilteredTensorWithIntegersModP.xml"> </Item> </Row>



<Row> <Item>
<Index>HomToIntegers</Index>
<#Include SYSTEM "newman/HomToIntegers.xml"> </Item> </Row>


<Row> <Item>
<Index>TensorWithIntegersModP</Index>
<#Include SYSTEM "newman/TensorWithIntegersModP.xml"> </Item> </Row>

</Table>

(Co)chain Complexes <M>\longrightarrow </M> Homotopy Invariants

<Table Align="|l|" >

<Row> <Item>
<Index>Cohomology</Index>
<#Include SYSTEM "newman/Cohomology.xml"> </Item> </Row>

<Row> <Item>
<Index>CupProduct</Index>
<#Include SYSTEM "newman/CupProduct.xml"> </Item> </Row>



<Row> <Item>
<Index>Homology</Index>
<#Include SYSTEM "newman/Homology.xml"> </Item> </Row>

</Table>


Visualization 

<Table Align="|l|" >

<Row> <Item>
<Index>BarCodeDisplay</Index>
<#Include SYSTEM "newman/BarCodeDisplay.xml"> </Item> </Row>

<Row> <Item>
<Index>BarCodeCompactDisplay</Index>
<#Include SYSTEM "newman/BarCodeCompactDisplay.xml"> </Item> </Row>

<Row> <Item>
<Index>CayleyGraphOfGroupDisplay</Index>
<#Include SYSTEM "newman/CayleyGraphOfGroupDisplay.xml"> </Item> </Row>


<Row> <Item>
<Index>Display</Index>
<#Include SYSTEM "newman/Display.xml"> </Item> </Row>

<Row> <Item>
<Index>DisplayArcPresentation</Index>
<#Include SYSTEM "newman/DisplayArcPresentation.xml"> </Item> </Row>

<Row> <Item>
<Index>DisplayCSVknotFile</Index>
<#Include SYSTEM "newman/DisplayCSVknotFile.xml"> </Item> </Row>



<Row> <Item>
<Index>DisplayDendrogram</Index>
<#Include SYSTEM "newman/DisplayDendrogram.xml"> </Item> </Row>

<Row> <Item>
<Index>DisplayDendrogramMat</Index>
<#Include SYSTEM "newman/DisplayDendrogramMat.xml"> </Item> </Row>

<Row> <Item>
<Index>DisplayPDBfile</Index>
<#Include SYSTEM "newman/DisplayPDBfile.xml"> </Item> </Row>


<Row> <Item> 
<Index>OrbitPolytope</Index>
<#Include SYSTEM "newman/OrbitPolytope.xml"> </Item> </Row>

<Row> <Item>
<Index>ScatterPlot</Index>
<#Include SYSTEM "newman/ScatterPlot.xml"> </Item> </Row>

</Table>
</Chapter>

