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<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>../tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>3</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> <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL>&nbsp;
</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>../tutorial/chap5.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.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="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/chap6.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap12.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap14.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutBogomolov.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGouter.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTensorSquare.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>19</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>../tutorial/chap5.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap6.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCohomologyRings.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGouter.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>17</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/chap4.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap8.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutNonabelian.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoefficientSequence.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/aboutLieCovers.html</Link><LinkText>11</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>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap8.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;
</Description> </ManSection> </Section> </Chapter>