#************************Creating Arrays***************************************
#These are the subroutines which create the arrays of 1s and 0s which represent the shadows of the top vertices.

sub h1is3 {
    my ($x1,$x2,$x3) = @_;
    for ($i=0; $i<=$x1; $i++) {
	for ($j=0; $j<=$x2; $j++) {
	    for ($k=0; $k<=$x3; $k++) {
		$countingarray[$i][$j][$k] = 1;
	    }
	}
    }
}

#*******************Counting Monomials********************************
#This section contains the subroutines which count the number of monomials of each degree.
#The input is the r^{h1}-dimensional array created in the subroutines in the previous section.


sub counth1is3 {
    my @osequence = (0);
    for ($q=1; $q<=$r; $q++) {
	@osequence = (@osequence,0);
    }
    for ($i=0; $i<=$r; $i++) {
	for ($j=0; $j<=$r; $j++) {
	    for ($k=0; $k<=$r; $k++) {
		if ($countingarray[$i][$j][$k]== 1) {
		    $osequence[$i+$j+$k]= $osequence[$i+$j+$k]+1;
		}
	    }
	}
    }

    use Tie::File;
    use Fcntl;
#here you will set the file to compare to
#change each oseqr#var#p# to reflect the rank, variable, and part
#change each compare_r#var#p# to reflect the rank, variable, and part
    tie @currentlist, Tie::File, oseqr4var3p15 or die "Can't tie file";
    tie @currentcompare, Tie::File, compare_r4var3p15 or die "Can't tie to file";

    my $string = "@osequence";
    my $yesorno = 0;

while ($yesorno == 0) {
    for ($i=0; $i<=$#currentcompare; $i++) {
	if ($string eq $currentcompare[$i]) {
	    $yesorno = 1;
	}
    }
    if ($yesorno == 0) {
	open (MYFILE, '>>compare_r4var3p15');
	print MYFILE "$string\n";
	close (MYFILE);

	open (MYFILE, '>>oseqr4var3p15');
	print MYFILE "(";
	    for ($i=0; $i<$r; $i++) {
		print MYFILE "@osequence[$i]";
		print MYFILE ",";
	    }
	print MYFILE "@osequence[$r]";
	print MYFILE ") & ";


#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#here we include the code to print the latex format to file

#***************************************
#h_r=15


print MYFILE "[";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array1[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array1[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array2[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array2[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array3[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array3[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array4[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array4[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array5[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array5[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array6[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array6[$h_1-1]";
print MYFILE "],";
print MYFILE "\\\\ & ";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array7[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array7[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array8[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array8[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array9[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array9[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array10[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array10[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array11[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array11[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array12[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array12[$h_1-1]";
print MYFILE "],";
print MYFILE "\\\\ & ";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array13[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array13[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array14[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array14[$h_1-1]";
print MYFILE "],";
print MYFILE "[";
for ($j=0; $j<$h1-1; $j++) {
  print MYFILE "@h_array15[$j]";
  print MYFILE ",";
}
print MYFILE "$h_array15[$h_1-1]";
print MYFILE "]]\\\\";
print MYFILE " & \\\\";


#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

	    print MYFILE "\n";

	    close (MYFILE);
	    $yesorno = 2;
	}
    }
}


#*************************************************************************
#This is the overall routine to generate the o-sequences
#Make sure that you:
#1. Change the vertex file you are tying to (@data =...)
#2. Change the rank to reflect the vertex file you are using
#3. Change the filenames in the subroutine 'counth1is#' to reflect how many vertices you are choosing in the topmost tier (let this number be k)
#4. Put in the appropriate number (k) of nested for loops so that you run through all subsets of k vertices

use Tie::File;
use Fcntl;

#here you will need to replace 'verticesr#var#' with your file of choice
tie @data, Tie::File, verticesr4var3 or die "Can't tie to file";

$possvert = $#data;
$r = 4; #here you will set the rank
$h1 = 3; #here you set the number of variables

#here you will add the appropriate number of for loops

#*********************************
#here h_r=15

for ($a1=0; $a1<=$possvert; $a1++) {

for ($a2=$a1+1; $a2<=$possvert; $a2++) {
for ($a3=$a2+1; $a3<=$possvert; $a3++) {
for ($a4=$a3+1; $a4<=$possvert; $a4++) {
for ($a5=$a4+1; $a5<=$possvert; $a5++) {
for ($a6=$a5+1; $a6<=$possvert; $a6++) {
for ($a7=$a6+1; $a7<=$possvert; $a7++) {
for ($a8=$a7+1; $a8<=$possvert; $a8++) {
for ($a9=$a8+1; $a9<=$possvert; $a9++) {
for ($a10=$a9+1; $a10<=$possvert; $a10++) {
for ($a11=$a10+1; $a11<=$possvert; $a11++) {
for ($a12=$a11+1; $a12<=$possvert; $a12++) {
for ($a13=$a12+1; $a13<=$possvert; $a13++) {
for ($a14=$a13+1; $a14<=$possvert; $a14++) {
for ($a15=$a14+1; $a15<=$possvert; $a15++) {

$vertex1=$data[$a1];
@h_array1=(split('',$vertex1));
$vertex2=$data[$a2];
@h_array2=(split('',$vertex2));
$vertex3=$data[$a3];
@h_array3=(split('',$vertex3));
$vertex4=$data[$a4];
@h_array4=(split('',$vertex4));
$vertex5=$data[$a5];
@h_array5=(split('',$vertex5));
$vertex6=$data[$a6];
@h_array6=(split('',$vertex6));
$vertex7=$data[$a7];
@h_array7=(split('',$vertex7));
$vertex8=$data[$a8];
@h_array8=(split('',$vertex8));
$vertex9=$data[$a9];
@h_array9=(split('',$vertex9));
$vertex10=$data[$a10];
@h_array10=(split('',$vertex10));
$vertex11=$data[$a11];
@h_array11=(split('',$vertex11));
$vertex12=$data[$a12];
@h_array12=(split('',$vertex12));
$vertex13=$data[$a13];
@h_array13=(split('',$vertex13));
$vertex14=$data[$a14];
@h_array14=(split('',$vertex14));
$vertex15=$data[$a15];
@h_array15=(split('',$vertex15));


@countingarray=();

h1is3(@h_array1);
h1is3(@h_array2);
h1is3(@h_array3);
h1is3(@h_array4);
h1is3(@h_array5);
h1is3(@h_array6);
h1is3(@h_array7);
h1is3(@h_array8);
h1is3(@h_array9);
h1is3(@h_array10);
h1is3(@h_array11);
h1is3(@h_array12);
h1is3(@h_array13);
h1is3(@h_array14);
h1is3(@h_array15);

counth1is3

}}}}}}}}}}}}}}}