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cohomology homomorphism functions
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grahamknockillaree committed Oct 14, 2023
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362 changes: 207 additions & 155 deletions doc/Undocumented.xml
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2 changes: 1 addition & 1 deletion doc/newAccess.xml
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</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>../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;
<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>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>8</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>
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4 changes: 2 additions & 2 deletions doc/newCubical.xml
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</Description> </ManSection>
<ManSection> <Func Name="Size" Arg="T"/> <Description> <P/> This returns the number of non-zero entries in the binary array of the cubical complex, or pure cubical complex T. <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/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutMetrics.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/aboutPeripheral.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/aboutQuandles2.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutKnots.html</Link><LinkText>19</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="Dimension" Arg="T"/> <Description> <P/> This returns the dimension of the cubical complex, or pure cubical complex T. <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;
<ManSection> <Func Name="Dimension" Arg="T"/> <Description> <P/> This returns the dimension of the cubical complex, or pure cubical complex T. <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>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTopology.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>8</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="WritePureCubicalComplexAsImage" Arg="T,str1,str2"/> <Description> <P/> Inputs a 2-dimensional pure cubical complex T, and a filename <M>str1</M> followed by its extension <M>str2</M> (e.g. <M>str1</M>="myfile" followed by <M>str2</M>="png"). A black/white image is saved to the file. <P/><B>Examples:</B>
</Description> </ManSection>
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</Description> </ManSection>
<ManSection> <Func Name="PureCubicalComplexToTextFile" Arg="file,M"/> <Description> <P/> Inputs a pure cubical complex <M>M</M> and a string containing the address of a file. A representation of this complex is written to the file in a format that can be read by the CAPD (Computer Assisted Proofs in Dynamics) software developed by Marian Mrozek and others. <P/><B>Examples:</B>
</Description> </ManSection>
<ManSection> <Func Name="ThickeningFiltration" Arg="M,n"/> <Func Name="ThickeningFiltration" Arg="M,n,k"/> <Description> <P/> Inputs a pure cubical complex <M>M</M> and a positive integer <M>n</M>. It returns a filtered pure cubical complex constructed frim <M>n</M> thickenings of <M>M</M>. If a positive integer <M>k</M> is supplied as an optional third argument, then each step of the filtration is obtained from a <M>k</M>-fold thickening. <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>1</LinkText></URL>&nbsp;
<ManSection> <Func Name="ThickeningFiltration" Arg="M,n"/> <Func Name="ThickeningFiltration" Arg="M,n,k"/> <Description> <P/> Inputs a pure cubical complex <M>M</M> and a positive integer <M>n</M>. It returns a filtered pure cubical complex constructed frim <M>n</M> thickenings of <M>M</M>. If a positive integer <M>k</M> is supplied as an optional third argument, then each step of the filtration is obtained from a <M>k</M>-fold thickening. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="Dendrogram" Arg="M"/> <Description> <P/> Inputs a filtered pure cubical complex <M>M</M> and returns data that specifies the dendrogram (or phylogenetic tree) describing how path components are born and then merge during the filtration. <P/><B>Examples:</B>
</Description> </ManSection>
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