FUNCTION: mchrepfin - test an algebra for being representation finite

CALLING SEQUENCE:
mchrepfin(a)
mchrepfin(a,s,p,m,c,incl,img)

PARAMETERS:
a - a completely separating bound poset algebra
s, p, m, c, incl, img - optional arguments evaluating to names

SYNOPSIS:

• mchrepfin tests whether its first argument, the bound poset algebra a, is of finite representation type.

• For mchrepfin to work properly, the algebra a has to be completely separating.

• Testing is done by constructing for each point s of the algebra the poset of minimal chain sequences starting in s and then testing this poset for finite representation type by looking for minimal non-representation finite (or critical) subposets.

• If the algebra is not of finite representation type, various data will be returned through the optional arguments. In particular:
  
  s - will be a point for which there is a poset of minimal chain sequences that is not of finite representation type.
  
  p - will contain the poset structure of the poset belonging to s.
  
  m - a table containing for each minimal chain sequence in p the corresponding s-start set.
  
  c - will give the name of the critical subposet of p found by the function.
  
  incl - a list containing data about the inclusion c --> p found by the function. In fact incl[i] is the image in p of the point i of c under this inclusion.
  
  img - a vector marking the points of p belonging to the image of c by 1, those not belonging to the image by 0.

EXAMPLES:

> a:=critical_alge(7,10);

> mchrepfin(a,'s','p','m','c','incl','img');

> print(s);

> print(p);

> print(m);

> print(c);

> print(incl);

> print(img);