Sophie: gap-system-4.4.12-5mdv2010.0 i586

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<html><head><title>[xgap] 5.6 GraphicSubgroupLattice, Inserting Vertices</title></head>
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<h1>5.6 GraphicSubgroupLattice, Inserting Vertices</h1><p>
<p>
To insert new vertices into a graphic sheet one has to use the
following operation:
<p>
<a name = "SSEC1"></a>
<li><code>InsertVertex( </code><var>sheet</var><code>, </code><var>grp</var><code>, </code><var>conj</var><code>, </code><var>hint</var><code> )</code>
<li><code>InsertVertex( </code><var>sheet</var><code>, </code><var>grp</var><code> )</code>
<p>
Inserts the group <var>grp</var> as a new vertex into the sheet. If the lattice
is <strong>not</strong>  the   subgroup lattice  of a  finitely  presented  group, it
checks, if the group is already in the lattice  or if there is already
a conjugate  subgroup.  Further,  the new  vertex is  sorted into  the
poset. So  <code>InsertVertex</code>  checks for  all vertices  on higher levels,
whether the new vertex  is contained,  and  for all vertices on  lower
levels, whether they are contained in the new vertex. It then tries to
add edges to the appropriate vertices.  If  the lattice is the lattice
of a  finitely presented group,  nothing is  done with respect  to the
connections of any vertex.  <code>InsertVertex</code> returns a list with the new
vertex as first entry and  a flag as  second, which says, whether this
vertex was inserted right now or has already  been there.  
<p>
<var>hint</var> is a list of <var>x</var> coordinates which should give some hint for
the choice of the new <var>x</var> coordinate. It can for example be the <var>x</var>
coordinates of those groups which were parameter for the operation
which calculated the group. <var>hints</var> can be empty but must always be a
list!
<p>
If <var>conj</var> is a vertex we put the new vertex into the class of this
vertex.  Otherwise <var>conj</var> should either be <code>false</code> or <code>fail</code>.
<p>
You have access to the simpler form of the above functions via the
<code>Subgroups</code> menu and the mouse. If you select 
<code>InsertVertices from GAP</code>
in the <code>Subgroups</code> menu, the function <code>InsertVertex</code> is called 
for the group in the (automatic) variable <code>last</code>, or, if <code>last</code>
contains a list of subgroups, for all of those subgroups. This is an
easy way to insert results of calculations with <font face="Gill Sans,Helvetica,Arial">GAP</font> into the
lattice. If <code>last</code> is neither a subgroup nor a list of subgroups,
nothing happens.
<p>
<p>
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<P>
<address>xgap manual<br>Mai 2003
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