FUNCTION: preproj - compute the beginning of the postprojective component of a bound poset algebra

CALLING SEQUENCE:
preproj(p)

PARAMETERS:
p - a bound poset algebra

SYNOPSIS:

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

• The program enters an interactive menue, asking for various additional information concerning its output.
  
  First the program asks, whether you wish to see the dimension vectors of the modules themselves, their tops or their socles, or whether you wish to terminate execution.
  During execution the program may repeatedly return to that menue. If you enter '0' here, you will leave the program and return to your CREP/Maple session.
  
  Next you may enter a visualization of the algebra p in such a way, that you may arrange the points of the algebra on a rectangular grid.
  If you choose this option, you are first asked for the size of the grid. Having answered that, you are asked to arrange the points of the algebra (labelled from 1 to p[1] - the number of points), filling vacant places with zeros.
  
  Next the program tells you, whether the algebra is separating, ('separating') whether it was able to compute a complete preprojective component containing all projectives and injectives ('repfinite') and whether it did stop knitting the component at some place ('cut').
  
  You then may take influence on the way, the Auslander Reiten quiver is printed in output. The orbits of the Auslander Reiten quiver are printed in columns, where two orbits may share the same column.
  
  If you choose to reorder the orbits, you first are asked for the number of columns (' length of section ?'). Then you may distribute orbits among the columns. Finally, being prompted for 'insertions' you may state, into which columns to fit the remaining orbits, giving first the number of the column, then that of the orbit.
  The neighbourhood-list of the orbitgraph of the Auslander-Reiten quiver printed before entering that menue may give a hint on how to rearrange the orbits.
  
  Finally you are asked for the number of Auslander Reiten translation to print.

• Output of the program is to a file called preproj.res, in the CREP home directory. (This is the directory Maple has to be invoked from for use of CREP.)

• All dialog will happen in the environment Maple was called from. So make sure, your current Maple session is not running in the background, when invoking preproj from Maple.

• The program preproj can also be invoked from the CREP home directory without using maple. In this case, the program also prompts for interactive input of the algebra p.

EXAMPLES:

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

> preproj(a);

which output (0=none,1=dim,2=top,3=soc,4=top+soc)?
1
visualization of the algebra (y/n) ?
y
number of rows ?
2
number of columns ?
3
1 2 3
1 2 3 4
2 0 1 0
separating repfinite cut
TRUE TRUE FALSE
orbit graph (by neighbours):
1: 2 3 4
2: 1
3: 1
4: 1
graduation of the orbit graph (start and stop numbers)
1 2 3 4
0 1 1 1
4 5 5 5
reordering of the tau-orbits (y/n) ?
y
length of section ?
3
1 2 3
2 3 4
insertions ?
2 1

number of tau translations ?
10
sincere !
more output (0=none,1=dim,2=top,3=soc,4=top+soc)?
0