with(coxeter):
read maxset;
read chrome;

# Find colorings for simply-laced graphs
# Select good inner products

# "good inner product" ie an inner product less than or equal to 0.
#  ie an edge
gip:=proc(i,j,pr) local c;
  c:=iprod(pr[i],pr[j]); if c<=0 then {i,j} fi;
end;

# set R to be the root system E6
R:=E6;
# suppress extraneous printing to the terminal
interface(quiet=true);
#  pr is the set of positive roots of R
#  X is a list containing the numbers 1 up to |pr|.
pr:=pos_roots(R): X:={$1..nops(pr)}:
#  constructs the graph as a list of edges 
G:={seq(seq(gip(j,i,pr),j=1..i-1),i=1..nops(pr))}: nops(G);
# uses maxset to get a list of all maximal independent 
# sets in order of decreasing size
mis:=maxset(G,X): nops(mis);
# uses chrome to ask for an 8-coloring
st:=time(): chrome(mis,X,8,'c'), c, .733*(time()-st);
# uses chrome to ask for a 9-coloring
st:=time(): chrome(mis,X,9,'c'), c, .733*(time()-st);
# resets interface and quits
#interface(quiet=false);
#quit;