<Chapter><Heading> Some functions for accessing basic data</Heading>

<Section><Heading> &nbsp;</Heading>

<ManSection>

<Func Name="BoundaryMap" Arg="C"/>
<Description>
<P/>

Inputs a resolution, chain complex or cochain complex <M>C</M>
and returns the function <M>C!.boundary</M>.
<P/><B>Examples:</B> <URL><Link>tutorial/chap2.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>2</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>
<ManSection>

<Func Name="BoundaryMatrix" Arg="C,n"/>
<Description>
<P/>

Inputs a chain or cochain complex <M>C</M> and integer <M>n</M>&tgt;<M>0</M>. It returns the <M>n</M>-th boundary map of <M>C</M> as a matrix.
<P/><B>Examples:</B> 
</Description>





















































































</ManSection>
<ManSection>

 
<Func Name="Dimension" Arg="C"/>

<Func Name="Dimension" Arg="M"/>
<Description>
<P/>

Inputs a resolution, chain complex or cochain complex <M>C</M>
and returns the function <M>C!.dimension</M> .
<P/>
Alternatively, inputs an <M>FpG</M>-module <M>M</M>
and returns its dimension as a vector space over the field of <M>p</M>
elements.
<P/><B>Examples:</B> <URL><Link>tutorial/chap3.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>3</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>4</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>5</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>6</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>7</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>
<ManSection>

<Func Name="EvaluateProperty" Arg="X,str"/>
<Description>
<P/>

Inputs a component object <M>X</M> 
(such as a <M>ZG</M>-resolution or chain map) and a string 
<M>str</M>="name" (such as "characteristic" or "type"). It searches <M>X.property</M> for the  pair ["name",value] and returns value. If <M>X.property</M>
does not exist, or if ["name",value] does not exist, it returns fail.
<P/><B>Examples:</B> 
</Description>





















































































</ManSection>

<ManSection>

<Func Name="GroupOfResolution" Arg="R"/>
<Description>
<P/>

Inputs a <M>ZG</M>-resolution <M>R</M> and returns the group <M>G</M>.
<P/><B>Examples:</B> 
</Description>





















































































</ManSection>
<ManSection>

<Func Name="Length" Arg="R"/>
<Description>
<P/>

Inputs a resolution <M>R</M> and returns its length 
(i.e. the number of terms of <M>R</M> that HAP has computed). 
<P/><B>Examples:</B> <URL><Link>tutorial/chap3.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap4.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap5.html</Link><LinkText>3</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap10.html</Link><LinkText>4</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>5</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutBogomolov.html</Link><LinkText>6</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>7</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>9</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>10</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>11</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>12</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutGouter.html</Link><LinkText>13</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTensorSquare.html</Link><LinkText>14</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>15</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>
<ManSection>

<Func Name="Map" Arg="f"/>
<Description>
<P/>

Inputs a chain map, or cochain map or equivariant chain map <M>f</M>
and returns the mapping function (as opposed to the 
target or the source of <M>f</M>) .
<P/><B>Examples:</B> <URL><Link>tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap4.html</Link><LinkText>3</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>4</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>5</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCohomologyRings.html</Link><LinkText>6</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>7</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>9</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>10</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutGouter.html</Link><LinkText>11</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>12</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>

<ManSection>

<Func Name="Source" Arg="f"/>
<Description>
<P/>

Inputs a chain map, or cochain map, or equivariant chain map, or 
<M>FpG</M>-module homomorphism <M>f</M> and returns it source.
<P/><B>Examples:</B> <URL><Link>tutorial/chap2.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>3</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutNonabelian.html</Link><LinkText>4</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>5</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>6</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>7</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>8</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>9</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>

<ManSection>

<Func Name="Target" Arg="f"/>
<Description>
<P/>

Inputs a chain map, or cochain map, or equivariant chain map, or 
<M>FpG</M>-module homomorphism <M>f</M> and returns its target.
<P/><B>Examples:</B> <URL><Link>tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>3</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>4</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>5</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>6</LinkText></URL>&nbsp; 

</Description>





















































































</ManSection>

</Section>
</Chapter>

