# EXAMPLE SCRIPT FOR THE POLYMAKE TUTORIAL LEIPZIG 2020
# -----------------------------------------------------
# DOMINIC BUNNETT TU BERLIN
# -----------------------------------------------------
# -----------------------------------------------------
#
# Upshot: 
# This script prints and saves tuples (x,y;j) such that
# Vol(j*Conv(0,x*e1,y*e2))>50
# for j minimal.
#
# In this script we loop over steadily growing simplic-
# es. For each simplex we define an indexing variable  
# "j".
# 
# Each iteration of the for loops starts with a 2 simp-
# lex defined by $p = convex_hull(0,x*e1,y*e2). We then
# check the volume of this simplex.
#
# If the volume is less than 51 we dilate the simplex 
# and check the volume again. We repeat this until the
# volume is greater than 50. 
#
# We then record in an array "@ar" the simplex we star-
# ted with and the dilation factor which brought us to
# volume above 50.
#
#
use application "polytope";

my $i=1;
my $n=10; 		# n gives us (roughly) the number of pairs we want to check!
my @ar=(); 

#we open an array where we are going to store data!

#we loop over all pairs (x,y):

for(my $x = 2; $x<$n-1; $x++){
    for(my $y = $x+1; $y<$n; $y++){

        #Then we define our simplex called $p and an indexing number "j":
           
         my $p = new Polytope(POINTS=>[[1,0,0],[1,$y,0],[1,0,$x]]);
         my $j = 1;
           
         if($p->VOLUME<51){
            my $small = true;
               
            while($small){
                  $j++;
                  my $next = new Polytope(POINTS=>[[1,0,0],[1,$j*$y,0],[1,0,$j*$x]]);
                  $small = $next->VOLUME<51;
           }
        }
        push @ar, new Vector([$x,$y,$j]);
        print "(x,y;j) = ($x,$y;$j) \n";
        $i++;
    }
}



my $mat = new Matrix(@ar);
save_data($mat,"2simplex_test.mat");