cyclic_chain_polytopes

#!/opt/homebrew/bin/perl
use strict;
use warnings;
use feature qw(say);

print "type anything to star the interactive shell";

while (<STDIN>) {
	say "What is n?";
	my $n = <STDIN>;
	chomp $n;
	last if $n eq '';
    say "What are the (maximal) chains?";
    my @arr;
    my $count = 0;
    while (my $line=<>)  {
    	chomp($line);
		last if $line eq '';
		push(@arr, [split(',',$line)]);
    }

sub chains_to_polytope1 {
	my @chains = @_;
	my @arr = map [(0) x ($n+1)], 1..@chains+2*$n;
	for (my $i = 0; $i < $n; $i++) {
		$arr[$i][$i+1] = 1;
		$arr[$i+$n][0] = 1;
		$arr[$i+$n][$i+1] = -1;
	}
	my $count = 2*$n;
	foreach my $c (@chains) {
		foreach my $entry (@$c) {
			$arr[$count][0] = 1;
			$arr[$count][$entry] = -1;
		}
		$count++;
	}
	return @arr;
}

sub right_circ_des {
	my @Y = @_;
	my $size = @Y;
	my $a = $Y[0];
	my $b = 0;
	my $cdesr = 0;
	for (my $i = 1; $i < $size; $i++) {
		if (($i == $size-1) & ($Y[$i] > $Y[0])) {
			$cdesr++;
			last;
		}
		$b = $Y[$i];
		if ($a > $b) {
			$cdesr++;
		}
		$a = $b;
	}
	return $cdesr;
}

#sub chains_to_polytope2 {
#	my @chains = @_;
#	my @arr = map [(0) x ($n+1)], 1..@chains+2*$n;
#	for (my $i = 0; $i < $n; $i++) {
#		$arr[$i][$i+1] = 1;
#		$arr[$i+$n][0] = 1;
#		$arr[$i+$n][$i+1] = -1;
#	}
#	my $count = 2*$n;
#	foreach my $c (@chains) {
#		$arr[$count][0] = right_circ_des(@$c);
#		foreach my $entry (@$c) {
#			$arr[$count][$entry] = -1;
#		}
#		$count++;
#	}
#	return @arr;
#}

sub print_matrix {
	my @arr = @_;
	for my $row (@arr) {
		say('['.join(',', @$row).'],');
	}
}

say "Flow polytope / Stanley's chain polytope construction:";
print_matrix(chains_to_polytope1(@arr));
# say "dual to Lauren's construction:";
# print_matrix(chains_to_polytope2(@arr));

}

1;