# ガウスの消去法 Gaussian Elimination
# 引数 方程式 (\@Equations)
# 戻り値 ガウスの消去法 (@GaussianElimination)
sub GAUSSIANELIMINATION{
	my ($Equations) = @_;
	my @SortEquations = @$Equations;
	my @TempEquations = ();
	my @GaussianElimination = ();
	my $Column = $#$Equations;
	my $Row = $#{$$Equations[0]};
	my $RowNumber = 0;
	
	# 配列数の確認
	for(my $i = 1; $i <= $Column; $i++){
		if($Row != $#{$$Equations[$i]}){
			return 0;
		}
	}
	if($Column != ($Row - 1)){
		return 0;
	}
	
	# 上三角行列 前進消去
	while($Column >= 0){
		# 降順ソート
		@SortEquations = sort {$b->[$RowNumber] <=> $a->[$RowNumber]} @SortEquations;
		# 行列の一番上 $SortEquations[0]をコピー
		$TempEquations[$RowNumber] = $SortEquations[0];
		last if($Column == 0);
	
		# $jの$RowNumber番目の要素を0にする
		for(my $j = 1; $j <= $Column; $j++){
			last if($SortEquations[$j][$RowNumber] == 0);
	
			my $Price0 = $SortEquations[0][$RowNumber];
			my $PriceJ = $SortEquations[$j][$RowNumber];
	
			for(my $k = $RowNumber; $k <= $Row; $k++){
				my $Diff = ($SortEquations[$j][$k] * $Price0) - ($SortEquations[0][$k] * $PriceJ);
	
				$SortEquations[$j][$k] = $Diff;
			}
		}
	
		# 行列の一番上 $SortEquations[0]を削除
		my @temp = @SortEquations;
		@SortEquations = ();
		for(my $j = 1; $j < @temp; $j++){
			$SortEquations[$j - 1] = $temp[$j];
		}
	
		# 行列の縦方向の要素数
		$Column = $#SortEquations;
	
		$RowNumber++;
	}
	
	# 後退代入
	$Column = $#$Equations;
	$Row = $#{$$Equations[0]};
	$GaussianElimination[$Row - 1] = $TempEquations[$Column][$Row] / $TempEquations[$Column][$Row - 1];
	for(my $i = $Column - 1; $i >= 0; $i--){
		my $tmp = $TempEquations[$i][$Row];
	
		for(my $j = $Row - 1; $j > $i; $j--){
			$tmp = $tmp - ($TempEquations[$i][$j] * $GaussianElimination[$j]);
		}
	
		# ガウスの消去法 Gaussian Elimination
		$GaussianElimination[$i] = $tmp / $TempEquations[$i][$i];
	}
	
	return @GaussianElimination;
}