[xgap] 5.8 GraphicSubgroupLattice, Poset Menu

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# 5.8 GraphicSubgroupLattice, Poset Menu

The `Poset` menu will be pulled down if you place the pointer inside the `Poset` button and press the left mouse button. Keep the button down and choose an entry by moving the pointer on top of this entry. Release the mouse button to select an entry.

This menu is a generic menu for any graphic poset and is not specific to subgroup lattices. So you find here options for the handling of general posets.

- `Redraw`

  The whole lattice will be redrawn. Use this option if some manipulation has disturbed the window.

- `Show Levels`

  If this menu entry is activated (after clicking it will have a small check sign at its right, clicking again deactivates it), there will be a little blue box under each level at the left edge of the graphic sheet. You can use these little boxes to change the height of a level by moving it up or down like a vertex. In cases where the order of the levels is not given by some ``external source'' like the index of the subgroups you can move levels by moving the corresponding blue box with pressed SHIFT button.

- `Show Levelparameters`

  This menu entry controls the display of the level parameters at the right edge of the graphic sheet. Normally these are displayed but you can switch it off with this menu entry.

- `Delete Vertices`

  Selecting the entry will delete all selected vertices. All edges from or to one of these are also deleted. However, inclusion information is preserved. This means that new edges are created from all vertices which were maximal in the deleted one to all vertices in which the deleted vertex was maximal. So you get the Hasse diagram of the poset which is the restriction of the former one to the not selected vertices.

- `Delete Edge`

  This menu entry is normally not selectable because it would destroy the Hasse diagram.

- `Merge Classes`

  This menu entry merges all classes within each level that contain a selected vertex. Afterwards `RearrangeClasses` (see below) is performed. Use `Merge Classes` to unite classes within a level, but use it with care: No further test is performed! If you unite classes of subgroups that are not conjugate, other errors may follow, because conjugacy tests are later on only performed by looking at the first subgroup in a given class!

- `Magnify Lattice`

  Selecting the entry will multiply the dimensions of the graphic sheet by the square root of 2 and enlarge the lattice accordingly.

- `Shrink Lattice`

  Selecting the entry will divide the dimensions of the graphic sheet by the square root of 2 and shrink the lattice accordingly.

- `Resize Lattice`

  Selecting this entry will pop up a dialog box asking for an x and y factor separated by a comma. You can enter integers or quotients. If you enter only one number this is used for x and y. The graphic sheet is then enlarged or shrinked and the lattice is resized accordingly.

- `Resize Sheet`

  This entry is similar to `Resize Lattice` except that only the graphic sheet is changed, the lattice remains unchanged. The numbers you enter must be integers and mean pixel numbers.

- `Change Labels`

  Selecting this entry will pop up a dialog box for each selected vertex asking for a new label. Clicking on CANCEL will cancel the relabelling of the remaining vertices but will not reset the already changed labels.

- `Average Y Positions`

  Selecting this entry will average the y coordinates of all vertices belonging to the same level. For graphic subgroup lattices this means all subgroups with the same index in the whole group.

- `Average X Positions`

  Selecting this entry will average the x coordinates of two or more selected vertices. This will only work if the corresponding subgroups do not have the same size and is used to align certain vertices vertically.

- `Rearrange Classes`

  Selecting this entry will clean up all classes which contain a selected vertex. You need this option if you have moved a vertex without its class (holding down the SHIFT key). The vertices in a class are arranged one next to the other horizontally without changing the order of the x coordinates. So you can permute the vertices within a class carelessly and then again get a nice picture with the new order by selecting this menu entry.

- `Use Black&White`

  Switches to black and white in case of a color screen or back to colors.

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