FUNCTION: xpreproj - frontend for preproj

CALLING SEQUENCE:
xpreproj(p)

PARAMETERS:
p - a bound poset algebra

SYNOPSIS:

• xpreproj passes the algebra p to an external program, which then tries to compute the beginning of a preprojective component of the Auslander-Reiten quiver of p.

• By executing xpreproj you get a window which is divided into three areas:
  • The first one, on the upper left of the window, encompasses the buttons 'apply' and 'end'. Pressing the 'apply' button executes the preproj algorithm with the arguments stated in the second area and then the output is given to the third area.

  • The second area gives you the possibility to rearrange the output of the preproj algorithm. After the label 'Which output?' you can vary the output of the dimension-vectors (see also 'help preproj'). Following that you can insert a number of tau-translations by moving the mouse pointer into the rectangle after the label and then typing in the desired amount. By pressing the 'reordering' button you receive a window in which you can type in the length of the section (see also 'help preproj'). Then a window named 'Reordering' is available. Here you insert the number which stands after the label 'Next:' into the table by clicking with the left mouse button in the upper row, these represent the orbit numbers. Each time you repeat this action the number after 'Next:' increases. Pressing the 'plus' and 'minus' button increases or decreases this number, respectively. After moving the mouse-pointer into the second line of the table behind the insertion label you can enter the number of the orbits to be inserted, these orbits are seperated by pressing 'return'. The 'cursor up', 'cursor down' and 'backspace' keys give you the possibility to edit your input. With 'done' you complete your reordering. The 'visualisation' button opens a window. This window enables you to define the width and the height of the table which appears once having pressed 'done'. In this table you place the points of your quiver (see 'help preproj'). To put a point into the table just press the left mouse button. The number which is thus fitted in is the number visible after the 'next' label, it increases each time the mouse button is depressed. With 'plus' and 'minus' you can control which number is inserted.

  • Hint: zero is an entry which leaves an empty space later in the output as well as in the table, so leave some columns empty to seperate the calculated entries of the dimension-vector.

  • The third area contains the output of the preproj algorithm.

EXAMPLES:

> a:=[4,[[1,2,3,4]]];

> xpreproj(a);