Chemistry::PointGroup::T - Point group T

package Chemistry::PointGroup::T;

use 5.008001;
use strict;
use warnings;

our $VERSION = '0.01';

my $h  = 12; # number of group elements
my @R  = qw( E C3 C3_2 C2 ); # symmetry elements of T
my @hi = qw( 1  4  4  3 ); # number of elements in the i-th class
my @I  = qw( A  E  T ); # irreducible representations
my %R;
@R{@R}=@hi;

# characters of the irreducible representations of T
my @A = qw( 1  1  1  1 );
my @E = qw( 2 -1 -1  2 );
my @T = qw( 3  0  0 -1 );

# my (%A, %E, %T);
# @A{@R} = @A; # A
# @E{@R} = @E; # E
# @T{@R} = @T; # T

sub new {
	my $type = shift;
	$type = ref($type) || $type;
	my %Ur   = @_;
	return bless \%Ur, $type;
}

sub character_tables {
return <<'TABLE';
+----+------------------------+-------+
|  T |  E   4C3  4C3_2  3C2   |       |
+----+------------------------+-------+
|  A |  1    1     1     1    |       |
|  E |  2   -1    -1     2    |       |
|  T |  3    0     0    -1    | x,y,x |
+----+------------------------+-------+  
TABLE
}

sub symmetry_elements {
	return @R;
}

sub normal_modes {
	my $self = shift;
	return (3 * $self->{E} - 6);
}

sub irr {
	my $self = shift;

	# proper operations   ( Ur - 2 ) (1 + 2 cos(r))
	my $X_E    = sprintf "%0.f",  ($self->{E}    - 2) * (1  + 2 * 1);
	my $X_C3   = sprintf "%0.f",  ($self->{C3}   - 2) * (1  + 2 * (-0.5));
	my $X_C3_2 = sprintf "%0.f",  ($self->{C3_2} - 2) * (1  + 2 * (-0.5));
	my $X_C2   = sprintf "%0.f",  ($self->{C2}   - 2) * (1  + 2 * (-1));
	
	# improper operations  Ur (-1 + 2 cos(r))
	
	# in the same order of @hi
	my @rr = ($X_E, $X_C3, $X_C3_2, $X_C2);
	
	# Irreducible representation
	my $s = 0;
	my $n_A = sprintf"%0.f", 
	(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A[$_] , $s] } (0..$#hi))[-1]->[1];

	$s = 0;
	my $n_E = sprintf"%0.f", 
	(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $E[$_] , $s] } (0..$#hi))[-1]->[1];

	$s = 0;
	my $n_T = sprintf"%0.f", 
	(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T[$_] , $s] } (0..$#hi))[-1]->[1];

	my @ri = ($n_A, $n_E, $n_T);
	my %ri = ();
	@ri{@I} = @ri;
	return %ri;
}
1;

__END__