To insert new vertices into a graphic sheet one has to use the following operation:
InsertVertex(
sheet,
grp,
conj,
hint )
InsertVertex(
sheet,
grp )
Inserts the group grp as a new vertex into the sheet. If the lattice
is not 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 InsertVertex
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. InsertVertex
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.
hint is a list of x coordinates which should give some hint for the choice of the new x coordinate. It can for example be the x coordinates of those groups which were parameter for the operation which calculated the group. hints can be empty but must always be a list!
If conj is a vertex we put the new vertex into the class of this
vertex. Otherwise conj should either be false
or fail
.
You have access to the simpler form of the above functions via the
Subgroups
menu and the mouse. If you select
InsertVertices from GAP
in the Subgroups
menu, the function InsertVertex
is called
for the group in the (automatic) variable last
, or, if last
contains a list of subgroups, for all of those subgroups. This is an
easy way to insert results of calculations with GAP into the
lattice. If last
is neither a subgroup nor a list of subgroups,
nothing happens.
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