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237 changes: 133 additions & 104 deletions doc/Undocumented.xml

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4 changes: 2 additions & 2 deletions doc/newCubical.xml

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2 changes: 1 addition & 1 deletion doc/newFunctors.xml
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</Description> </ManSection>
<ManSection> <Func Name="LowerCentralSeriesLieAlgebra" Arg="G"/> <Func Name="LowerCentralSeriesLieAlgebra" Arg="f"/> <Description> <P/> Inputs a pcp group <M>G</M>. If each quotient <M>G_c/G_{c+1}</M> of the lower central series is free abelian or p-elementary abelian (for fixed prime p) then a Lie algebra <M>L(G)</M> is returned. The abelian group underlying <M>L(G)</M> is the direct sum of the quotients <M>G_c/G_{c+1}</M> . The Lie bracket on <M>L(G)</M> is induced by the commutator in <M>G</M>. (Here <M>G_1=G</M>, <M>G_{c+1}=[G_c,G]</M> .) <P/> The function can also be applied to a group homomorphism <M>f: G \longrightarrow G'</M> . In this case the induced homomorphism of Lie algebras <M>L(f):L(G) \longrightarrow L(G')</M> is returned.<P/> If the quotients of the lower central series are not all free or p-elementary abelian then the function returns fail.<P/> This function was written by Pablo Fernandez Ascariz <P/><B>Examples:</B> <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLie.html</Link><LinkText>3</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="TensorWithIntegers" Arg="X"/> <Description> <P/> Inputs either a <M>ZG</M>-resolution <M>X=R</M>, or an equivariant chain map <M>X = (F:R \longrightarrow S)</M>. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers (characteristic 0). <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArtinGroups.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAspherical.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutParallel.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/aboutCocycles.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPolytopes.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoxeter.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRosenbergerMonster.html</Link><LinkText>19</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>20</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>21</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>22</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutExtensions.html</Link><LinkText>23</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSpaceGroup.html</Link><LinkText>24</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>25</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGraphsOfGroups.html</Link><LinkText>26</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>27</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>28</LinkText></URL>&nbsp;
<ManSection> <Func Name="TensorWithIntegers" Arg="X"/> <Description> <P/> Inputs either a <M>ZG</M>-resolution <M>X=R</M>, or an equivariant chain map <M>X = (F:R \longrightarrow S)</M>. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers (characteristic 0). <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap3.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap6.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArtinGroups.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAspherical.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutParallel.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCocycles.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPolytopes.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoxeter.html</Link><LinkText>19</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRosenbergerMonster.html</Link><LinkText>20</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>21</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>22</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>23</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutExtensions.html</Link><LinkText>24</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSpaceGroup.html</Link><LinkText>25</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>26</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGraphsOfGroups.html</Link><LinkText>27</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>28</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>29</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="FilteredTensorWithIntegers" Arg="R"/> <Description> <P/> Inputs a <M>ZG</M>-resolution <M>R</M> for which "filteredDimension" lies in NamesOfComponents(R). (Such a resolution can be produced using TwisterTensorProduct(), ResolutionNormalSubgroups() or FreeGResolution().) It returns the filtered chain complex obtained by tensoring with the trivial module of integers (characteristic 0). <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>&nbsp;
</Description> </ManSection>
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2 changes: 1 addition & 1 deletion doc/newHomology.xml
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</Description> </ManSection>
<ManSection> <Func Name="BarCodeDisplay" Arg="P"/> <Func Name="BarCodeDisplay" Arg="P,str"/> <Func Name="BarCodeCompactDisplay" Arg="P"/> <Func Name="BarCodeCompactDisplay" Arg="P,str"/> <Description> <P/> Inputs an integer persistence matrix P, and an optional string, such as <M>str</M>="mozilla" specifying a viewer/browser. It displays a picture of the bar code (using GraphViz software). The compact display is better for large bar codes. <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.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="Homology" Arg="X,n"/> <Description> <P/> Inputs either a chain complex <M>X=C</M> or a chain map <M>X=(C \longrightarrow D)</M>. <List> <Item>If <M>X=C</M> then the torsion coefficients of <M>H_n(C)</M> are retuned.</Item> <Item> If <M>X=(C \longrightarrow D)</M> then the induced homomorphism <M>H_n(C) \longrightarrow H_n(D)</M> is returned as a homomorphism of finitely presented groups. </Item> </List> A <M>G</M>-complex <M>C</M> can also be input. The homology groups of such a complex may not be abelian. <B>Warning:</B> in this case Homology(C,n) returns the abelian invariants of the <M>n</M>-th homology group of <M>C</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/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap5.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap9.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap12.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutMetrics.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArtinGroups.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAspherical.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutParallel.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>19</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCocycles.html</Link><LinkText>20</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>21</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>22</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>23</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>24</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPolytopes.html</Link><LinkText>25</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoxeter.html</Link><LinkText>26</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>27</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>28</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>29</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRosenbergerMonster.html</Link><LinkText>30</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>31</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>32</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>33</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutExtensions.html</Link><LinkText>34</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSpaceGroup.html</Link><LinkText>35</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>36</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGraphsOfGroups.html</Link><LinkText>37</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>38</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTensorSquare.html</Link><LinkText>39</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>40</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>41</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLie.html</Link><LinkText>42</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTwistedCoefficients.html</Link><LinkText>43</LinkText></URL>&nbsp;
<ManSection> <Func Name="Homology" Arg="X,n"/> <Description> <P/> Inputs either a chain complex <M>X=C</M> or a chain map <M>X=(C \longrightarrow D)</M>. <List> <Item>If <M>X=C</M> then the torsion coefficients of <M>H_n(C)</M> are retuned.</Item> <Item> If <M>X=(C \longrightarrow D)</M> then the induced homomorphism <M>H_n(C) \longrightarrow H_n(D)</M> is returned as a homomorphism of finitely presented groups. </Item> </List> A <M>G</M>-complex <M>C</M> can also be input. The homology groups of such a complex may not be abelian. <B>Warning:</B> in this case Homology(C,n) returns the abelian invariants of the <M>n</M>-th homology group of <M>C</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/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap5.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap6.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap9.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap12.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutMetrics.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArtinGroups.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAspherical.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutParallel.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>19</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>20</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCocycles.html</Link><LinkText>21</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>22</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>23</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>24</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>25</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPolytopes.html</Link><LinkText>26</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoxeter.html</Link><LinkText>27</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>28</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>29</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>30</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRosenbergerMonster.html</Link><LinkText>31</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>32</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>33</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>34</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutExtensions.html</Link><LinkText>35</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSpaceGroup.html</Link><LinkText>36</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>37</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGraphsOfGroups.html</Link><LinkText>38</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>39</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTensorSquare.html</Link><LinkText>40</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>41</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>42</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLie.html</Link><LinkText>43</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTwistedCoefficients.html</Link><LinkText>44</LinkText></URL>&nbsp;
</Description> </ManSection>
<ManSection> <Func Name="HomologyPb" Arg="C,n"/> <Description> <P/> This is a back-up function which might work in some instances where <M>Homology(C,n)</M> fails. It is most useful for chain complexes whose boundary homomorphisms are sparse. <P/> It inputs a chain complex <M>C</M> in characteristic <M>0</M> and returns the torsion coefficients of <M>H_n(C)</M> . There is a small probability that an incorrect answer could be returned. The computation relies on probabilistic Smith Normal Form algorithms implemented in the Simplicial Homology GAP package. This package therefore needs to be loaded. The computation is stored as a component of <M>C</M> so, when called a second time for a given <M>C</M> and <M>n</M>, the calculation is recalled without rerunning the algorithm. <P/> The choice of probabalistic algorithm can be changed using the command <P/> SetHomologyAlgorithm(HomologyAlgorithm[i]);<P/> where i = 1,2,3 or 4. The upper limit for the probability of an incorrect answer can be set to any rational number <M>0</M>&tlt;<M>e</M>&tlt;= <M>1</M> using the following command. <P/>SetUncertaintyTolerence(e);<P/> See the Simplicial Homology package manual for further details. <P/><B>Examples:</B>
</Description> </ManSection>
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