The graphical interface for the xpre family

Getting started

Executing the command xpre(a), xpre(Q), or xpre(p) starts the calculation of a preprojective component of the algebra given by a, Q, or p respectively, if such a component exists, and, after displaying some information about the calculation done, the Auslander-Reiten-Quiver (dimension vectors and arrows) is drawn in a separate window. You can then edit the appearance of the quiver and the dimension vectors as you like. It is also possible to print the quiver to a text file or a postscript file.

Main Window

The Main Window is divided into the following parts: the Pulldown Menus, the Quit Button, and the Main Viewing Area.

Pulldown Menus

  View Menu

• Orbit Graph

  Clicking on Orbit Graph displays a window with information about the orbit graph of the AR-Quiver. Basically it is just the incidence matrix of the preprojective component quiver, together with the number of arrows between two orbits. For example, P(1) : 3(2) in the first row of the table means that the tau-orbit of the indecomposable projective module corresponding to point no. 1 has two arrows to the tau-orbit of P(3).

  By clicking on the rows of the table the corresponding orbit is highlighted in the Viewing Area of the Main Window.

  You can hide the Orbit Graph Window by clicking the Close Button.

• General Info

  The menu button General Info redisplays the messages shown at the start of the program. There are stored some information about the type of the preprojective component, for example which of the indecomposable projective modules have been found.

  You can hide the General Info Window by clicking the Close Button.

• Order Dimension Vector

  Here you can change the appearance of the dimension vectors. When selecting this menu item a window with buttons ordered in a big square pops up. By clicking on one of the buttons with a number on it, you "pick up" the number, i.e., the entry of the dimension vector corresponding to this number, and drop it wherever you want (inside the dialog window of course!) by clicking on an empty button. By pressing Apply the changes are applied without closing the dialog, by pressing Done the changes are applied and the window is closed. Cancel closes the dialog window without any changes, but not if you have already chosen Apply before.

• Hide Dimension Vector

  Clicking on this menu item hides the dimension vector and displays bullets instead. This is very convenient when you order the orbits of the AR-Quiver or want to get an overview of the structure of the quiver.

• Number of Modules

  Here a dialog window is displayed with an input field where you can enter an arbitrary number. This is the maximum number of modules to be displayed. Often there are so many modules shown that the display is slowed down considerably. You can speed up the display by typing 100 or 500 into this input field. Moreover, the space the dimension vector occupies on the screen is less after this because the entries are smaller numbers.

  Press Cancel to leave without changes or press Return or the OK button to apply the changes.

• Set Column Width

  This menu item starts a dialog box with a scrollbar which controls the distance between the dimension vectors displayed. As before, by clicking Apply you can view the changes without closing the window, and Done applies the changes and closes the dialog. By pressing Cancel you leave the dialog without changes.

• Text File

  After clicking on the item Text File there pops up a File Selector window where you choose a text file to save the data in.

  See also: File Selector.

  The data is stored as follows: First the Orbit Graph is displayed, as in the Orbit Graph window, to give the information about the arrows. Then the beginning of the preprojective component is printed, as on the screen, up to the numbers of modules you chose in the menu item Number of Modules.

• Postscript File

  This is the recommended output for xpre. This menu item shows a File Selector window where you can choose the output file. See also: File Selector.

  There is an extra button labelled Settings in the File Selector window. By clicking this button another dialog is displayed where you can choose the paper size and the magnification of the postscript output. By pressing Done you hide this dialog and get back to the File Selector window.

  When you have selected a postscript file, the AR-Quiver displayed in the Viewing Area of the Main Window is written to this file as it is on the screen (with the magnification you selected taken into account). In particular, if you chose to hide the dimension vectors, the postscript output will also display only points and arrows. The pages are ordered the following way: If the quiver is to big to fit on one page or on one row of pages, then the output is printed row after row.

  You can view postscript files with Ghostview for example, or ask your system administrator about your local installation.

Viewing Area In the Viewing Area, which occupies most of the Main Window, the calculated AR-Quiver is shown. With the scroll bars at the right and bottom of the window you can scroll to the part of the quiver you wish to see.
It is possible to rearrange the vertical position of the orbits by drag and drop. First click with the middle mouse button on one of the dimension vectors (or points) in the orbit you want to move. It is then highlighted in yellow (or any other color, depending on your system). Now drag it to the desired position by depressing and holding down the right mouse button. Drop it there by releasing the right mouse button.
It is also possible to select an orbit for ragging via the Orbit Graph Window. If you select a line in the table displayed there the corresponding orbit in the Viewing Area is highlighted at the same time and vice versa. See also: Pulldown Menus -> View Menu -> Orbit Graph above.
The horizontal position can only be changed by manipulating the width of the "columns" of the quiver. How to do this is described in detail in the section Pulldown Menus -> Options Menu -> Set Column Width above.

Orbit Graph Window

The Orbit Graph window is described in section Pulldown Menus -> View Menu -> Orbit Graph.

General Info Window

The General Info window is described in section Pulldown Menus -> View Menu -> General Info.

File Selector

Here you can select the file you want to read or where you want to save your file. This window appears in some graphical user interfaces in CREP.
Description: At the top of the File Selector window the current Directory and a pattern is shown. In the area below this all directories and all files of the current directory which match the pattern are shown. If there are changes in the directory you can force an update of the view with the Rescan button.
You can either select a file by a left mouse click or directly type the name of the file at the bottom of the window.
If you have selected a file to load or save press the enter key or the Ready button in the window.
Finally there is a Cancel button which closes the File Selector window and nothing is changed.
You can also navigate through the File Selector window with the arrow keys and the enter key of your keyboard.