[xgap] 5.6 GraphicSubgroupLattice, Inserting Vertices

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# 5.6 GraphicSubgroupLattice, Inserting Vertices

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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